MODELO DE ANALITICA DE DATOS - ASEGURAMIENTO EN SALUD - DEPARTAMENTO DE CUNDINAMARCA
Derian Jesús Dorado-Daza
06/2023
INTRODUCCION
El presente recurso desarrolla un modelo de analÃtica de datos que tiene como propósito la identificación de tendencias o relaciones entre las variables de los afiliados al Sistema de Salud en el departamento de Cundinamarca, de tal modo que permita apoyar decisiones tendientes al mejoramiento de la cobertura y acceso a los servicios de salud; Se consolidó un dataset multidimensional con 13 caracterÃsticas de los afiliados y el número de afiliados en cada variable que atiende cada prestador de salud. Para la implementación del modelo se recurrió a los algoritmos de clustering que propone la Ciencia de Datos. Después de un proceso de evaluación de los algoritmos K-means, Clustering Jerárquico, y K-medoids, las métricas empleadas permitieron determinar que el algoritmo K-means presenta el mejor desempeño. Como resultado se obtuvieron 4 clusters estables que reflejan las relaciones o tendencias entre caracterÃsticas de afiliados y prestadores de servicios de salud.
1.- EXPLORACION Y COMPRENSION DE LOS DATOS
1.1.- Análisis Univariado
El dataset contiene el listado de los prestadores de servicios de salud públicos y privados que operan en el departamento y la cantidad (conteo) de usuarios que atienden distribuidos en diferentes variables (grupos etarios, sexo, nivel socioeconómico y zona de residencia).
# Cargue del dataset y paqueterÃa necesaria.
library(readxl)
require(ggplot2)
require(plotly)
require(CGPfunctions)
require(ggpubr)
library(factoextra)
library(broom)
library(pander)
library(corrplot)
library(gridExtra)
library(reshape)
library(reshape2)
library(dplyr)
library(tidyr)
library(corrplot)
library(Hmisc)
library(tidyverse)
library(rgl)
library(igraph)
library(fpc)
library(fpc)
library(NbClust)
library(cluster)
library(amap)
library(clustertend)
library(clValid)
data_aseg <- read_excel("data_aseg_202305.xlsx")
attach(data_aseg)
summary(data_aseg)## nom_ips_prim cod_ips total_ips Primera_infancia
## Length:240 Length:240 Min. : 1.0 Min. : 0.00
## Class :character Class :character 1st Qu.: 727.5 1st Qu.: 48.75
## Mode :character Mode :character Median : 3734.5 Median : 271.00
## Mean : 8477.4 Mean : 580.92
## 3rd Qu.:10355.0 3rd Qu.: 632.25
## Max. :94785.0 Max. :6484.00
## Infancia Adolescencia Juventud Adultez
## Min. : 0.00 Min. : 0.0 Min. : 0 Min. : 0.0
## 1st Qu.: 57.75 1st Qu.: 54.5 1st Qu.: 114 1st Qu.: 250.2
## Median : 302.00 Median : 351.5 Median : 610 Median : 1456.0
## Mean : 698.72 Mean : 787.1 Mean : 1492 Mean : 3535.8
## 3rd Qu.: 772.75 3rd Qu.: 916.0 3rd Qu.: 1671 3rd Qu.: 4162.0
## Max. :8492.00 Max. :9576.0 Max. :18743 Max. :41843.0
## Adulto_mayor F M Nivel_1
## Min. : 0.0 Min. : 0.0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 127.8 1st Qu.: 357.2 1st Qu.: 333.2 1st Qu.: 227.5
## Median : 701.0 Median : 1903.0 Median : 1894.0 Median : 1431.0
## Mean : 1382.9 Mean : 4297.9 Mean : 4179.5 Mean : 2577.6
## 3rd Qu.: 1619.5 3rd Qu.: 5212.8 3rd Qu.: 5049.5 3rd Qu.: 3068.8
## Max. :10692.0 Max. :47933.0 Max. :46852.0 Max. :20491.0
## Nivel_2 Nivel_3 Rural Urbano
## Min. : 0.00 Min. : 0.0 Min. : 0.00 Min. : 0
## 1st Qu.: 75.25 1st Qu.: 20.0 1st Qu.: 86.75 1st Qu.: 422
## Median : 649.00 Median : 144.0 Median : 900.00 Median : 2208
## Mean : 1672.38 Mean : 664.9 Mean : 1632.28 Mean : 6845
## 3rd Qu.: 2142.50 3rd Qu.: 629.8 3rd Qu.: 2229.00 3rd Qu.: 6527
## Max. :24509.00 Max. :12125.0 Max. :11019.00 Max. :92322
## nat cod_mun mun cod_ipss_prim
## Length:240 Min. : 1.0 Length:240 Min. :2.500e+11
## Class :character 1st Qu.:269.0 Class :character 1st Qu.:2.527e+11
## Mode :character Median :404.5 Mode :character Median :2.540e+11
## Mean :478.7 Mean :2.548e+11
## 3rd Qu.:754.0 3rd Qu.:2.575e+11
## Max. :899.0 Max. :2.590e+11
## lat long
## Min. :3.919 Min. :-74.81
## 1st Qu.:4.559 1st Qu.:-74.46
## Median :4.834 Median :-74.24
## Mean :4.795 Mean :-74.22
## 3rd Qu.:5.046 3rd Qu.:-74.03
## Max. :5.620 Max. :-73.24head(data_aseg)| nom_ips_prim | cod_ips | total_ips | Primera_infancia | Infancia | Adolescencia | Juventud | Adultez | Adulto_mayor | F | M | Nivel_1 | Nivel_2 | Nivel_3 | Rural | Urbano | nat | cod_mun | mun | cod_ipss_prim | lat | long |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| HOSPITAL MARIO GAITAN YANGUAS - EMPRESA SOCIAL DEL ESTADO REGION DE SALUD SOACHA | e_1 | 49662 | 5413 | 4434 | 4828 | 8185 | 18610 | 8192 | 26481 | 23181 | 20491 | 7150 | 736 | 8435 | 41227 | pub | 754 | SOACHA | 2.5754e+11 | 4.581866 | -74.24030 |
| EMPRESA SOCIAL DEL ESTADO HOSPITAL SAN RAFAEL DE FUSAGASUGA | e_2 | 35624 | 2413 | 2815 | 3201 | 5802 | 14319 | 7074 | 18511 | 17113 | 15722 | 6295 | 1002 | 5350 | 30274 | pub | 290 | FUSAGASUGA | 2.5290e+11 | 4.323534 | -74.38859 |
| E.S.E. HOSPITAL SAN RAFAEL DE PACHO - (255130002801) | e_3 | 24116 | 1440 | 1851 | 2339 | 3363 | 9013 | 6110 | 12131 | 11985 | 12687 | 5134 | 1509 | 9068 | 15048 | pub | 513 | PACHO | 2.5513e+11 | 5.168368 | -74.16337 |
| EMPRESA SOCIAL DEL ESTADO HOSPITAL SAN JOSE DE GUADUAS | e_4 | 21856 | 1062 | 1510 | 1987 | 2906 | 8790 | 5601 | 10686 | 11170 | 13209 | 3252 | 973 | 9215 | 12641 | pub | 320 | GUADUAS | 2.5320e+11 | 5.173555 | -74.64015 |
| EMPRESA SOCIAL DEL ESTADO E.S.E MUNICIPAL DE SOACHA JULIO CESAR PEñALOZA - SEDE SAN MARCOS (257540007501) | e_5 | 17477 | 1782 | 1892 | 1832 | 2278 | 6245 | 3448 | 9964 | 7513 | 7918 | 2642 | 237 | 1821 | 15656 | pub | 754 | SOACHA | 2.5754e+11 | 4.581866 | -74.24030 |
| HOSPITAL MARIA AUXILIADORA EMPRESA SOCIAL DE ESTADO DEL MUNICIPIO DE MOSQUERA | e_6 | 15258 | 1341 | 1096 | 1218 | 2990 | 6059 | 2554 | 7949 | 7309 | 4106 | 3401 | 726 | 773 | 14485 | pub | 473 | MOSQUERA | 2.5473e+11 | 4.672714 | -74.23573 |
# DISTRIBUCION DE AFILIADOS POR PRESTADORES DE SERVICIOS DE SALUD EN EL DEPARTAMENTO
barplot(height=total_ips, names=cod_ips,col=c('red'),ylim=c(0,80000))
# VARIABLES DE GRUPO ETARIO
data_aseg_ge <-subset(data_aseg, select = c("Primera_infancia","Infancia","Adolescencia","Juventud","Adultez","Adulto_mayor"))
data_aseg_1 <- melt(data_aseg_ge)
conteo_tot <- aggregate(value ~ variable, data_aseg_1, sum)
ggplot(data_aseg_1, aes(x = variable, y = value, fill=variable)) + geom_bar(stat="identity")+geom_text(data = conteo_tot, aes(x = variable, y = value, label = value, group = 1),
position = position_stack(vjust = 0.5), color = "white", size = 4) +
xlab("Variable") +
ylab("Value") +
ggtitle("Total por cada grupo etario")
#Boxplot Variables de Grupo Etario
ggplot(data_aseg_1, aes(x = variable, y = value, color=variable)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor") +
theme_minimal()
# VARIABLES DE GENERO
data_aseg_s <-subset(data_aseg, select = c("F","M"))
data_aseg_2 <- melt(data_aseg_s)
conteo_tot <- aggregate(value ~ variable, data_aseg_2, sum)
ggplot(data_aseg_2, aes(x = variable, y = value, fill=variable)) + geom_bar(stat="identity")+geom_text(data = conteo_tot, aes(x = variable, y = value, label = value, group = 1),
position = position_stack(vjust = 0.5), color = "white", size = 4) +
xlab("Variable") +
ylab("Value") +
ggtitle("Total por cada Género")
#Boxplot Variables de Género
ggplot(data_aseg_2, aes(x = variable, y = value, color=variable)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor") +
theme_minimal()
# VARIABLES DE NIVEL SOCIOECONOMICO
data_aseg_n <-subset(data_aseg, select = c("Nivel_1","Nivel_2","Nivel_3"))
data_aseg_3 <- melt(data_aseg_n)
conteo_tot <- aggregate(value ~ variable, data_aseg_3, sum)
ggplot(data_aseg_3, aes(x = variable, y = value, fill=variable)) + geom_bar(stat="identity")+geom_text(data = conteo_tot, aes(x = variable, y = value, label = value, group = 1),
position = position_stack(vjust = 0.5), color = "white", size = 4) +
xlab("Variable") +
ylab("Value") +
ggtitle("Total por cada Nivel Socioeconómico")
#Boxplot Variables de Grupo Etario
ggplot(data_aseg_3, aes(x = variable, y = value, color=variable)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor") +
theme_minimal()
# VARIABLES DE ZONA
data_aseg_z <-subset(data_aseg, select = c("Rural","Urbano"))
data_aseg_4 <- melt(data_aseg_z)
conteo_tot <- aggregate(value ~ variable, data_aseg_4, sum)
ggplot(data_aseg_4, aes(x = variable, y = value, fill=variable)) + geom_bar(stat="identity")+geom_text(data = conteo_tot, aes(x = variable, y = value, label = value, group = 1),
position = position_stack(vjust = 0.5), color = "white", size = 4) +
xlab("Variable") +
ylab("Value") +
ggtitle("Total por Zona de residencia")
#Boxplot Variables de Zona
ggplot(data_aseg_4, aes(x = variable, y = value, color=variable)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor") +
theme_minimal()
1.2.- Medida de Correlaciones
# Columna 2 como indice
data_aseg_c <- data_aseg %>% column_to_rownames(., var = 'cod_ips')
# remocion de la columnas/variables informativas nom_ips_prim, total_ips y nat
data_aseg_c$nom_ips_prim <- NULL
data_aseg_c$total_ips <- NULL
data_aseg_c$nat <- NULL
data_aseg_c$cod_mun <- NULL
data_aseg_c$mun <- NULL
data_aseg_c$cod_ipss_prim <- NULL
data_aseg_c$lat <- NULL
data_aseg_c$long <- NULL
# Normalización de los datos
data_aseg_norm <- scale(data_aseg_c)
# Prueba de Boxplot luego de la estandarizacion
#data_aseg_nz <-subset(data_aseg_norm, select = c("Rural","Urbano"))
#data_aseg_12 <- melt(data_aseg_nz)
#data_aseg_12
#conteo_tot12 <- aggregate(value ~ Var2, data_aseg_12, sum)
#ggplot(data_aseg_12, aes(x = Var2, y = value, color=Var2)) +
# geom_boxplot() +
# labs(x = "Variable", y = "Valor") +
# theme_minimal()
# MEDICION DE LAS CORRELACION ENTRE LAS VARIABLES
# Matriz de Correlaciones y Estimacion del P-Valor
rcorr(as.matrix(data_aseg_norm))## Primera_infancia Infancia Adolescencia Juventud Adultez
## Primera_infancia 1.00 0.99 0.98 0.97 0.97
## Infancia 0.99 1.00 1.00 0.98 0.99
## Adolescencia 0.98 1.00 1.00 0.97 0.99
## Juventud 0.97 0.98 0.97 1.00 0.99
## Adultez 0.97 0.99 0.99 0.99 1.00
## Adulto_mayor 0.82 0.81 0.82 0.82 0.85
## F 0.98 0.99 0.99 0.98 1.00
## M 0.98 0.99 0.99 0.99 1.00
## Nivel_1 0.84 0.81 0.82 0.77 0.79
## Nivel_2 0.92 0.92 0.92 0.96 0.94
## Nivel_3 0.76 0.79 0.79 0.85 0.84
## Rural 0.41 0.37 0.40 0.39 0.38
## Urbano 0.97 0.98 0.98 0.98 0.99
## Adulto_mayor F M Nivel_1 Nivel_2 Nivel_3 Rural Urbano
## Primera_infancia 0.82 0.98 0.98 0.84 0.92 0.76 0.41 0.97
## Infancia 0.81 0.99 0.99 0.81 0.92 0.79 0.37 0.98
## Adolescencia 0.82 0.99 0.99 0.82 0.92 0.79 0.40 0.98
## Juventud 0.82 0.98 0.99 0.77 0.96 0.85 0.39 0.98
## Adultez 0.85 1.00 1.00 0.79 0.94 0.84 0.38 0.99
## Adulto_mayor 1.00 0.88 0.87 0.85 0.79 0.70 0.53 0.84
## F 0.88 1.00 1.00 0.82 0.93 0.83 0.40 0.99
## M 0.87 1.00 1.00 0.83 0.95 0.83 0.43 0.98
## Nivel_1 0.85 0.82 0.83 1.00 0.70 0.48 0.69 0.76
## Nivel_2 0.79 0.93 0.95 0.70 1.00 0.91 0.44 0.92
## Nivel_3 0.70 0.83 0.83 0.48 0.91 1.00 0.28 0.83
## Rural 0.53 0.40 0.43 0.69 0.44 0.28 1.00 0.27
## Urbano 0.84 0.99 0.98 0.76 0.92 0.83 0.27 1.00
##
## n= 240
##
##
## P
## Primera_infancia Infancia Adolescencia Juventud Adultez
## Primera_infancia 0 0 0 0
## Infancia 0 0 0 0
## Adolescencia 0 0 0 0
## Juventud 0 0 0 0
## Adultez 0 0 0 0
## Adulto_mayor 0 0 0 0 0
## F 0 0 0 0 0
## M 0 0 0 0 0
## Nivel_1 0 0 0 0 0
## Nivel_2 0 0 0 0 0
## Nivel_3 0 0 0 0 0
## Rural 0 0 0 0 0
## Urbano 0 0 0 0 0
## Adulto_mayor F M Nivel_1 Nivel_2 Nivel_3 Rural Urbano
## Primera_infancia 0 0 0 0 0 0 0 0
## Infancia 0 0 0 0 0 0 0 0
## Adolescencia 0 0 0 0 0 0 0 0
## Juventud 0 0 0 0 0 0 0 0
## Adultez 0 0 0 0 0 0 0 0
## Adulto_mayor 0 0 0 0 0 0 0
## F 0 0 0 0 0 0 0
## M 0 0 0 0 0 0 0
## Nivel_1 0 0 0 0 0 0 0
## Nivel_2 0 0 0 0 0 0 0
## Nivel_3 0 0 0 0 0 0 0
## Rural 0 0 0 0 0 0 0
## Urbano 0 0 0 0 0 0 0correlacion=cor(data_aseg_norm)
# Representación gráfica de la matriz de correlaciones
corrplot(correlacion, method="color")
2.- PREPARACION DE LOS DATOS
2.1.- Análisis de Componentes Principales (PCA)
#ANALISIS DE COMPONENTES Y ESTANDARIZACION DEL DATASET (media=0 y DS=1)
data_aseg_pca <- prcomp(data_aseg_c, scale = TRUE)
# VERIFICACION DE LOS COMPONENTES PRINCIPALES
#data_aseg_pca$rotation
#head(data_aseg_pca$x)
# Representación gráfica
#Calidad de la representación de los individuos
fviz_pca_ind(data_aseg_pca, geom = c("point", "text"), axes=c(1, 2), pointsize=1.5, col.ind="cos2", repel=TRUE)
# Representacion de individuos, dimensiones y variables
fviz_pca_biplot(data_aseg_pca, repel=TRUE, ggtheme=theme_grey())+labs(title ="Representacion PCA-Biplot")
# Zoom sobre el sector mas denso de variables
fviz_pca_biplot(data_aseg_pca, repel=TRUE, ggtheme=theme_grey())+labs(title ="Representacion PCA-Biplot")+xlim(c(-7,0))+ylim(c(0,-2))
# Representacion 3D
plot3d(data_aseg_pca$x[,1:3],type="s", col="red", size=1)
rglwidget()# Representacion de los individuos, variables
fviz_pca_biplot(data_aseg_pca, repel=TRUE, ggtheme=theme_grey(),habillage=data_aseg$nat,
addEllipses=TRUE, ellipse.level=0.995, palette = "Dark2")+labs(title ="Representacion PCA-Biplot")
# Zoom sobre el sector mas denso de individuos
fviz_pca_biplot(data_aseg_pca, repel=TRUE, ggtheme=theme_grey(),habillage=data_aseg$nat,
palette = "Dark2")+labs(title ="Representacion PCA-Biplot")+xlim(c(0,3))+ylim(c(-2, 2))
# Varianza por cada componente principal
data_aseg_pca$sdev^2## [1] 1.109543e+01 1.093001e+00 4.581846e-01 2.370770e-01 3.979207e-02
## [6] 3.725522e-02 1.814010e-02 1.606949e-02 2.966315e-03 1.077809e-03
## [11] 1.003314e-03 4.646964e-32 1.473382e-32# Proporcion de Varianza explicada
p_varianza <- data_aseg_pca$sdev^2 / sum(data_aseg_pca$sdev^2)
p_varianza## [1] 8.534949e-01 8.407700e-02 3.524497e-02 1.823669e-02 3.060928e-03
## [6] 2.865786e-03 1.395392e-03 1.236115e-03 2.281781e-04 8.290840e-05
## [11] 7.717800e-05 3.574588e-33 1.133371e-33# Grafico de Dimensiones vs Varianza Explicada
fviz_eig(data_aseg_pca, addlabels = TRUE, ylim = c(0, 90))
#Calidad` de representación de las variables
fviz_cos2(data_aseg_pca, choice = "var", axes = 1:2)
fviz_pca_var(data_aseg_pca, col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE
)
3.- DESARROLLO DEL MODELO
3.1.- Verificación preliminar de existencia de agrupaciones en los datos
# Validacion de tendencia sobre el dataset con el estadistico de Hopkins
# PREVIO A PCA
library(clustertend)
set.seed(321)
hopkins(data_aseg_norm, n = nrow(data_aseg_norm) - 1)## $H
## [1] 0.06757716# Validacion de estructura en los datos empleando la matriz de distancias
matriz_dist_aseg <- dist(data_aseg_norm, method = "euclidean")
estructura <- fviz_dist(dist.obj = matriz_dist_aseg, show_labels = FALSE) +
labs(title = "Datos") + theme(legend.position = "bottom")
estructura
# POSTERIOR A PCA - Dos dimensiones principales
set.seed(321)
hopkins(data_aseg_pca$x[,1:2], n = nrow(data_aseg_pca$x[,1:2]) - 1)## $H
## [1] 0.1051677# Validacion de estructura en los datos empleando la matriz de distancias
matriz_dist_aseg_pca <- dist(data_aseg_pca$x[,1:2], method = "euclidean")
estructura_pca <- fviz_dist(dist.obj = matriz_dist_aseg, show_labels = FALSE) +
labs(title = "Datos") + theme(legend.position = "bottom")
estructura_pca
3.2.- Modelo basado en K-Means
3.2.1.- Determinación del número óptimo de clusters y evaluación del modelo K-means
# Prueba preliminar de determinación del número optimo de clusters mediante WSS
#set.seed(123)
#suma_cuadrados <- c()
#for (i in 1:30) {
# k <- kmeans(data_aseg_pca$x[,1:2], centers = i)
# suma_cuadrados[i] <- k$tot.withinss
#}
#plot(1:30, suma_cuadrados, type = "b", xlab = "Número de clusters", ylab = "Suma de las distancias al cuadrado")
#Determinacion del numero K optimo de clusters con FactoExtra y nbclust().
## Metodo del Codo con diferentes distancias
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "euclidean")) + labs(subtitle = "Metodo del Codo_ Dist-Euclidean") 
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "manhattan")) + labs(subtitle = "Metodo del Codo_Dist-Manhattan") 
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "pearson")) + labs(subtitle = "Metodo del Codo_Dist-Pearson") 
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "spearman")) + labs(subtitle = "Metodo del Codo_Dist-Spearman") 
## Metodo de la Silueta con diferentes distancias
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "silhouette", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "euclidean")) + labs(subtitle = "Metodo de la Silueta-Euclidean")
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "silhouette", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "manhattan")) + labs(subtitle = "Metodo de la Silueta-Manhattan")
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "silhouette", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "pearson")) + labs(subtitle = "Metodo de la Silueta-Pearson")
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method = "silhouette", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "spearman")) + labs(subtitle = "Metodo de la Silueta-Spearman")
## Metodo Gap Statistic con diferentes distancias
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method ="gap_stat", nstart=30, k.max=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "euclidean")) + labs(subtitle = "Metodo Gap Stat-Euclidean")
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method ="gap_stat", nstart=30, k.max=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "manhattan")) + labs(subtitle = "Metodo Gap Stat-Manhattan")
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method ="gap_stat", nstart=30, k.max=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "Pearson")) + labs(subtitle = "Metodo Gap Stat-Pearson")
fviz_nbclust(data_aseg_pca$x[,1:2], kmeans, method ="gap_stat", nstart=30, k.max=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "Spearman")) + labs(subtitle = "Metodo Gap Stat-Spearman")
#EVALUACION modelo K-means
# Ancho de la Silueta - modelo K-means
km_clusters <- eclust(x = data_aseg_pca$x[,1:2], FUNcluster = "kmeans", k = 4, seed = 123,
hc_metric = "euclidean", nstart=30, graph = FALSE)
fviz_silhouette(sil.obj = km_clusters, print.summary = TRUE, palette = "jco",
ggtheme = theme_classic()) ## cluster size ave.sil.width
## 1 1 14 0.42
## 2 2 53 0.26
## 3 3 9 0.28
## 4 4 164 0.69
head(km_clusters$silinfo$widths)| cluster | neighbor | sil_width | |
|---|---|---|---|
| ip_11 | 1 | 2 | 0.5611304 |
| e_2 | 1 | 2 | 0.5593445 |
| ip_10 | 1 | 2 | 0.5494646 |
| ip_18 | 1 | 2 | 0.5255848 |
| ip_17 | 1 | 2 | 0.5191313 |
| ip_14 | 1 | 2 | 0.4477604 |
# Indice Dunn
km_indiceD <- cluster.stats(d = dist(data_aseg_pca$x[,1:2], method = "euclidean"), clustering=km_clusters$cluster)
km_indiceD$average.within## [1] 1.418568km_indiceD$average.between## [1] 5.523847km_indiceD$dunn## [1] 0.01376138# Indice de Davies Bouldin - modelo K-means
library(clusterSim)
print(index.DB(data_aseg_pca$x[,1:2], km_clusters$cluster, centrotypes="centroids"))## $DB
## [1] 0.8510354
##
## $r
## [1] 0.8536798 0.8483910 0.8536798 0.8483910
##
## $R
## [,1] [,2] [,3] [,4]
## [1,] Inf 0.8448702 0.8536798 0.4008493
## [2,] 0.8448702 Inf 0.5044677 0.8483910
## [3,] 0.8536798 0.5044677 Inf 0.3508599
## [4,] 0.4008493 0.8483910 0.3508599 Inf
##
## $d
## 1 2 3 4
## 1 0.000000 4.50365 7.625935 7.293469
## 2 4.503650 0.00000 11.804159 2.791510
## 3 7.625935 11.80416 0.000000 14.459905
## 4 7.293469 2.79151 14.459905 0.000000
##
## $S
## [1] 2.1801446 1.6248547 4.3299627 0.7434373
##
## $centers
## [,1] [,2]
## [1,] -5.606005 1.1771764
## [2,] -1.166614 0.4191048
## [3,] -12.864465 -1.1615525
## [4,] 1.561554 -0.1721893# Conectividad Modelo K-means
d = dist(data_aseg_pca$x[,1:2], method = "euclidean")
connectivity(d,km_clusters$cluster,neighbSize = 10)## [1] 26.67817# Estabilidad - modelo K-means
estabilidad_k<-clValid(data_aseg_norm, 4, clMethods = "kmeans",
validation = "stability", maxitems = 600,
metric = "euclidean")
summary(estabilidad_k)##
## Clustering Methods:
## kmeans
##
## Cluster sizes:
## 4
##
## Validation Measures:
## 4
##
## kmeans APN 0.0048
## AD 1.7953
## ADM 0.0428
## FOM 0.4653
##
## Optimal Scores:
##
## Score Method Clusters
## APN 0.0048 kmeans 4
## AD 1.7953 kmeans 4
## ADM 0.0428 kmeans 4
## FOM 0.4653 kmeans 4# Evaluación del modelo con los criterios jitter-boot
test.clusterboot<-clusterboot(data_aseg_pca$x[,1:2],B=70,bootmethod=c("jitter","boot"),clustermethod=kmeansCBI, krange=4, seed=123)## jitter 1
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## boot 70test.clusterboot## * Cluster stability assessment *
## Cluster method: kmeans
## Full clustering results are given as parameter result
## of the clusterboot object, which also provides further statistics
## of the resampling results.
## Number of resampling runs: 70
##
## Number of clusters found in data: 4
##
## Clusterwise Jaccard jittering mean:
## [1] 1.0000000 0.9966028 0.9883117 0.9887218
## dissolved:
## [1] 0 0 0 0
## recovered:
## [1] 70 70 67 67
## Clusterwise Jaccard bootstrap (omitting multiple points) mean:
## [1] 0.8349219 0.9014838 0.7454673 0.7032363
## dissolved:
## [1] 7 0 14 18
## recovered:
## [1] 48 60 37 293.2.2.- Ejecución del modelo K-means
# Clustering
# Clusters_pca <- Kmeans(data_aseg_pca$x[,1:2], 4, method="euclidean")
#clusters_pca <- kmeans(data_aseg_pca$x[,1:2], 4)
#clusters_pca
fviz_cluster(km_clusters,data_aseg_pca$x[,1:2]) #op2: clusters_pca
plot3d(data_aseg_pca$x[,1:3],type="s", col=km_clusters$cluster, size=1) #op2: clusters_pca$cluster
rglwidget()# Asignación de clusters al dataset
datos_cluster_pca <- data.frame(data_aseg, cluster = as.factor(km_clusters$cluster)) #clusters_pcs$cluster
write.csv(datos_cluster_pca, "mi_KmC_4K_20230620-1700.csv")
# ANALISIS DE LOS CLUSTERS
# Tamaño de los clusters en relacion a los afiliados que atienden los prestadores
data_aseg_cl_afil <-subset(datos_cluster_pca, select = c("total_ips","cluster"))
data_aseg_cl_afil_1<- data_aseg_cl_afil %>%
group_by(cluster) %>%
summarise(total_afil=sum(total_ips)) %>%
mutate(porcentaje_ta = total_afil/ sum(total_afil) * 100)
ggplot(data_aseg_cl_afil_1, aes(x = cluster, y = total_afil, fill=cluster)) + geom_bar(stat="identity") + geom_text(aes(label = paste0(round(porcentaje_ta), "%\n", total_afil)), vjust = 3) 
# Distribucion Prestadores Publicos y Privados en los clusters
data_aseg_nat <-subset(datos_cluster_pca, select = c("nat","cluster"))
data_aseg_nat_porcent <- data_aseg_nat %>%
group_by(cluster,nat) %>%
summarise(count=n()) %>%
mutate(porcentaje = count / sum(count) * 100)
ggplot(data_aseg_nat_porcent, aes(x = "", y = porcentaje, fill=nat)) + geom_bar(stat="identity",width = 1) +
coord_polar("y", start = 0) +
facet_wrap(~cluster) +
theme_void() +
labs(x = NULL, y = NULL, fill = "nat") +
geom_text(aes(label = paste0(round(porcentaje), "%\n", count)), position = position_stack(vjust = 0.5))
# Grupos Etarios
data_aseg_gk <-subset(datos_cluster_pca, select = c("Primera_infancia","Infancia","Adolescencia","Juventud","Adultez","Adulto_mayor","cluster"))
data_aseg_gk_porcent <- data_aseg_gk %>%
group_by(cluster) %>%
summarise(across(c(Primera_infancia,Infancia,Adolescencia,Juventud,Adultez,Adulto_mayor), sum)) %>%
mutate(across(c(Primera_infancia,Infancia,Adolescencia,Juventud,Adultez,Adulto_mayor), function(x) x / sum(x) * 100))
data_aseg_gk1 <- melt(data_aseg_gk_porcent, id.vars = "cluster")
ggplot(data_aseg_gk1, aes(x = variable, y = value, fill=cluster)) + geom_bar(stat="identity",position = "stack") + geom_text(aes(label = paste0(round(value, 1), "%")), position = position_stack(vjust = 0.5), color = "white")
#Boxplot de Clusters versus las variables de Grupos Etarios
data_aseg_gk2 <- melt(data_aseg_gk)
ggplot(data_aseg_gk2, aes(x = variable, y = value, fill = cluster)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor", fill = "Cluster") +
theme_minimal()
# Sexo
data_aseg_sk <-subset(datos_cluster_pca, select = c("F","M","cluster"))
data_aseg_sk_porcent <- data_aseg_sk %>%
group_by(cluster) %>%
summarise(across(c(F,M,), sum)) %>%
mutate(across(c(F,M), function(x) x / sum(x) * 100))
data_aseg_sk1 <- melt(data_aseg_sk_porcent, id.vars = "cluster")
ggplot(data_aseg_sk1, aes(x = variable, y = value, fill=cluster)) + geom_bar(stat="identity",position = "stack") + geom_text(aes(label = paste0(round(value, 1), "%")), position = position_stack(vjust = 0.5), color = "white")
#Boxplot de Clusters versus las variables de Género
data_aseg_sk2 <- melt(data_aseg_sk)
ggplot(data_aseg_sk2, aes(x = variable, y = value, fill = cluster)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor", fill = "Cluster") +
theme_minimal()
# Nivel Socioeconomico
data_aseg_nk <-subset(datos_cluster_pca, select = c("Nivel_1","Nivel_2","Nivel_3","cluster"))
data_aseg_nk_porcent <- data_aseg_nk %>%
group_by(cluster) %>%
summarise(across(c(Nivel_1,Nivel_2,Nivel_3), sum)) %>%
mutate(across(c(Nivel_1,Nivel_2,Nivel_3), function(x) x / sum(x) * 100))
data_aseg_nk1 <- melt(data_aseg_nk_porcent, id.vars = "cluster")
ggplot(data_aseg_nk1, aes(x = variable, y = value, fill=cluster)) + geom_bar(stat="identity",position = "stack") + geom_text(aes(label = paste0(round(value, 1), "%")), position = position_stack(vjust = 0.5), color = "white")
#Boxplot de Clusters versus las variables de Nivel Socioeconomico
data_aseg_nk2 <- melt(data_aseg_nk)
ggplot(data_aseg_nk2, aes(x = variable, y = value, fill = cluster)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor", fill = "Cluster") +
theme_minimal()
# Zona
data_aseg_zk <-subset(datos_cluster_pca, select = c("Rural","Urbano","cluster"))
data_aseg_zk_porcent <- data_aseg_zk %>%
group_by(cluster) %>%
summarise(across(c(Rural,Urbano), sum)) %>%
mutate(across(c(Rural,Urbano), function(x) x / sum(x) * 100))
data_aseg_zk1 <- melt(data_aseg_zk_porcent, id.vars="cluster")
ggplot(data_aseg_zk1, aes(x = variable, y = value, fill=cluster)) + geom_bar(stat="identity",position = "stack") + geom_text(aes(label = paste0(round(value, 1), "%")), position = position_stack(vjust = 0.5), color = "white")
#Boxplot de Clusters versus las variables de Nivel Socioeconomico
data_aseg_zk2 <- melt(data_aseg_zk)
ggplot(data_aseg_zk2, aes(x = variable, y = value, fill = cluster)) +
geom_boxplot() +
labs(x = "Variable", y = "Valor", fill = "Cluster") +
theme_minimal()
3.3.- Modelo basado en Clustering Jerárquico
3.3.1.- Determinación del número óptimo de clusters y evaluación del modelo Clustering Jerárquico
# Determinación de la mejor estructura para el Dendograma a partir de la correlación entre distancias originales y distancias del Dendograma.
matriz_dist <- dist(x = data_aseg_pca$x[,1:2], method = "euclidean") # method: euclidean, manhattan
hc_dl_ward <- hclust(d = matriz_dist, method = "single") # method: single,complete, average, ward
cor(x = matriz_dist, cophenetic(hc_dl_ward))## [1] 0.9462142# DETERMINACION DEL NUMERO OPTIMO DE CLUSTERS PARA EL MODELO BASADO EN CLUSTERING JERARQUICO
# Método Gráfico. Observando el punto de corte en el dendograma
hc_euclidea_single <- hclust(d = dist(x=data_aseg_pca$x[,1:2], method="euclidean"),method="single")
fviz_dend(x = hc_euclidea_single, k = 1, cex = 0.6, show_labels=FALSE) +
geom_hline(yintercept = 3.2, linetype = "dashed") +
labs(title = "Clustering Jerárquico", subtitle = "Distancia Manhattan, Linkage Ward")
# Empleando la librerÃa NbClust() y variando los hiperparámetros distancia y método
# Distancia EuclÃdea y varios linkage
testH.nbclust_single <- NbClust(data_aseg_pca$x[,1:2], distance="euclidean", min.nc=2, max.nc=30, method="single", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 9 proposed 2 as the best number of clusters
## * 2 proposed 3 as the best number of clusters
## * 6 proposed 5 as the best number of clusters
## * 1 proposed 10 as the best number of clusters
## * 3 proposed 11 as the best number of clusters
## * 1 proposed 21 as the best number of clusters
## * 1 proposed 24 as the best number of clusters
## * 1 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_single## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 1.2110 48.6294 30.7199 -16.6876 68.7971 2080310 2630470.33 2418.8114
## 3 1.4687 42.6332 33.4613 -19.1743 112.2717 3905176 1921788.95 2142.2946
## 4 0.7132 43.4048 133.6979 -28.3906 156.4042 5776407 1529582.40 1877.2509
## 5 2.1139 84.0625 16.8337 -23.4437 336.8583 4255349 760872.97 1198.3600
## 6 0.6854 75.1131 2.1426 -24.9786 357.7335 5617238 659894.86 1118.2560
## 7 1.6885 63.2530 13.5704 -27.1668 360.3148 7563891 645744.90 1108.1096
## 8 0.5991 59.0586 0.2943 -28.2607 376.6688 9228598 562577.57 1047.1232
## 9 0.4347 51.5555 112.5972 -30.0696 378.2332 11604057 562615.81 1045.7967
## 10 3.1212 80.3263 53.7959 -25.1674 520.1388 7931185 266992.39 703.0878
## 11 1.8199 94.1712 5.1567 -23.2732 597.4925 6952601 149776.21 569.8117
## 12 0.7867 87.6224 0.7704 -24.3566 621.6371 7482268 149273.06 557.2630
## 13 4.7095 80.3024 13.6896 -25.6432 622.9010 8735149 148372.50 555.3863
## 14 0.2200 79.2977 0.2706 -25.9475 661.9650 8608969 128692.26 523.7979
## 15 1.2614 73.4148 3.1447 -27.1054 662.5682 9857935 128269.88 523.1715
## 16 0.8229 69.3781 0.5226 -27.9923 679.6850 10444066 127946.53 515.9602
## 17 1.0027 64.9352 0.4953 -29.0068 680.9663 11727593 127642.61 514.7591
## 18 1.0012 61.0056 0.4551 -29.9714 681.8733 13098296 126863.48 513.6183
## 19 0.9832 57.4996 0.2265 -30.8929 683.0040 14525494 126600.41 512.5675
## 20 0.5729 54.2942 32.6172 -31.7897 684.1661 16016986 126615.91 512.0428
## 21 1.9943 60.5809 0.1454 -30.4675 783.4755 11674893 89301.71 445.9293
## 22 1.0404 57.4777 0.4962 -31.3031 783.7103 12800735 89200.06 445.6334
## 23 0.9644 54.7602 0.1361 -32.0826 786.0727 13853842 88770.26 444.6214
## 24 16.3929 52.1765 8.4378 -32.8603 786.8087 15038524 88668.45 444.3427
## 25 0.0452 52.0652 21.6703 -33.0163 798.6747 15530686 82166.62 427.6376
## 26 4.8994 55.6273 10.9142 -32.2383 840.1967 14129303 71795.30 388.4817
## 27 6.9942 56.3708 8.2709 -32.1723 870.6276 13422546 68603.63 369.6303
## 28 0.0492 56.4310 0.1085 -32.2713 894.4690 13070165 66156.82 355.8139
## 29 2.2175 54.1905 10.6735 -32.9448 895.2023 13977648 66161.14 355.6319
## 30 0.4743 55.0744 0.1048 -32.8321 909.2952 14105176 58900.49 338.5084
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale Ratkowsky
## 2 0.2986 1.2043 0.1662 0.1428 0.8432 0.8857 30.5908 0.1285 0.2432
## 3 0.5365 1.3598 0.1578 0.2605 0.7211 0.9478 12.9338 0.0548 0.2567
## 4 0.7943 1.5518 0.1811 0.2277 0.7307 0.6381 132.7118 0.5647 0.2515
## 5 2.3146 2.4309 0.2206 0.3668 0.7585 0.9685 7.4493 0.0324 0.2825
## 6 2.5948 2.6050 0.2408 0.3736 0.6912 0.2093 11.3367 2.8342 0.2623
## 7 2.6280 2.6288 0.2408 0.2823 0.6962 0.9830 3.9514 0.0173 0.2438
## 8 2.8360 2.7819 0.2597 0.2800 0.6640 150.1282 0.0000 0.0000 0.2337
## 9 2.8503 2.7855 0.2597 0.2531 0.6678 0.6715 111.0717 0.4872 0.2208
## 10 5.7032 4.1432 0.2187 0.4012 0.6537 0.8032 53.4036 0.2439 0.2216
## 11 6.7234 5.1123 0.2580 0.4183 0.6655 0.4562 8.3432 1.0429 0.2356
## 12 7.0386 5.2274 0.2579 0.3865 0.6620 16.1084 -0.9379 -0.4690 0.2303
## 13 7.0765 5.2451 0.2579 0.3594 0.6631 0.9855 3.1535 0.0146 0.2214
## 14 7.4464 5.5614 0.3011 0.3528 0.6359 85.4573 0.0000 0.0000 0.2212
## 15 7.4535 5.5680 0.3011 0.3240 0.6416 0.3039 11.4530 1.9088 0.2138
## 16 7.6980 5.6459 0.3010 0.2973 0.6458 11.1639 -1.8209 -0.6070 0.2092
## 17 7.7331 5.6590 0.3010 0.2778 0.6337 14.8400 -0.9326 -0.4663 0.2031
## 18 7.7464 5.6716 0.3011 0.2463 0.6325 23.2289 -0.9570 -0.4785 0.1975
## 19 7.7775 5.6832 0.3011 0.2379 0.6346 44.1054 -0.9773 -0.4887 0.1922
## 20 7.7988 5.6890 0.3011 0.2213 0.6410 0.8706 31.7939 0.1479 0.1875
## 21 9.0706 6.5325 0.2846 0.2411 0.5519 254.8684 0.0000 0.0000 0.1933
## 22 9.0779 6.5368 0.2846 0.2312 0.5575 10.5721 -2.7162 -0.6791 0.1889
## 23 9.1131 6.5517 0.2846 0.2325 0.5351 78.7103 0.0000 0.0000 0.1849
## 24 9.1243 6.5558 0.2846 0.2147 0.5380 1.0047 -0.9689 -0.0046 0.1811
## 25 9.5103 6.8119 0.2803 0.2165 0.5181 0.9083 21.0043 0.1005 0.1777
## 26 10.9410 7.4985 0.2881 0.2127 0.5348 0.9539 9.9613 0.0481 0.1754
## 27 12.0537 7.8809 0.2830 0.2117 0.5434 0.9652 7.3982 0.0359 0.1730
## 28 13.0379 8.1870 0.2787 0.2133 0.5412 566.9647 0.0000 0.0000 0.1704
## 29 13.0605 8.1912 0.2787 0.2044 0.5438 0.9545 9.7250 0.0474 0.1675
## 30 13.5945 8.6055 0.3068 0.2031 0.5515 109.1975 0.0000 0.0000 0.1651
## Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex SDbw
## 2 1209.4057 0.4644 45.1353 0.0011 0.3393 8e-04 2.8432 2.2319 0.4329
## 3 714.0982 0.5188 -1.9584 0.0047 0.1916 8e-04 1.9115 2.1032 0.2894
## 4 469.3127 0.6120 5.2770 0.0060 0.1987 8e-04 1.5333 2.0092 0.2051
## 5 239.6720 0.7752 7.6795 0.0137 0.2717 8e-04 1.4509 1.7103 0.1559
## 6 186.3760 0.7847 177.7625 0.0155 0.2116 7e-04 1.5360 1.6607 0.1196
## 7 158.3014 0.7837 9.4072 0.0156 0.1946 7e-04 1.5674 1.6433 0.0684
## 8 130.8904 0.7863 -181.0508 0.0175 0.1952 7e-04 2.0072 1.6003 0.0573
## 9 116.1996 0.7861 7.4501 0.0175 0.1882 7e-04 2.4183 1.5935 0.0671
## 10 70.3088 0.7842 2.9448 0.0357 0.1853 7e-04 2.4584 1.3402 0.0488
## 11 51.8011 0.8001 26.0111 0.0405 0.2338 7e-04 2.3945 1.2436 0.0625
## 12 46.4386 0.7991 -1067.8377 0.0407 0.1961 7e-04 2.3579 1.2246 0.0336
## 13 42.7220 0.7990 4.1130 0.0407 0.1941 7e-04 2.3822 1.2186 0.0274
## 14 37.4141 0.7996 -59.3017 0.0426 0.2118 7e-04 2.2742 1.1914 0.0250
## 15 34.8781 0.7995 65.0962 0.0426 0.1961 7e-04 3.3158 1.1867 0.0220
## 16 32.2475 0.7985 -80.4640 0.0428 0.1947 7e-04 3.3503 1.1701 0.0178
## 17 30.2799 0.7982 -87.2771 0.0429 0.1785 7e-04 3.3771 1.1658 0.0157
## 18 28.5343 0.7980 -75.3418 0.0429 0.1770 7e-04 3.4654 1.1611 0.0137
## 19 26.9772 0.7978 -43.5942 0.0429 0.1544 7e-04 3.4503 1.1571 0.0117
## 20 25.6021 0.7976 8.8152 0.0430 0.1487 7e-04 4.4551 1.1525 0.0158
## 21 21.2347 0.7631 -31.0557 0.0559 0.1362 7e-04 4.3922 1.0742 0.0103
## 22 20.2561 0.7630 -52.6468 0.0559 0.1354 7e-04 5.1219 1.0710 0.0093
## 23 19.3314 0.7626 -30.2783 0.0560 0.1324 7e-04 5.0837 1.0658 0.0084
## 24 18.5143 0.7626 5.5107 0.0560 0.1314 7e-04 5.3436 1.0627 0.0076
## 25 17.1055 0.7587 3.9569 0.0584 0.1283 7e-04 5.3896 1.0412 0.0070
## 26 14.9416 0.7552 3.6854 0.0626 0.1228 7e-04 5.4352 0.9965 0.0063
## 27 13.6900 0.7537 5.0400 0.0647 0.1226 7e-04 6.0229 0.9742 0.0058
## 28 12.7076 0.7498 -23.1838 0.0671 0.1137 7e-04 6.2553 0.9551 0.0054
## 29 12.2632 0.7497 3.6912 0.0671 0.1132 7e-04 6.6182 0.9526 0.0050
## 30 11.2836 0.7477 -22.2239 0.0692 0.1255 7e-04 6.7054 0.9315 0.0046
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.5221 216.9679 0.8794
## 3 0.5214 215.7172 0.9467
## 4 0.5211 215.0914 0.5689
## 5 0.5193 211.9589 0.9681
## 6 -0.4219 -10.1102 0.1360
## 7 0.5190 211.3316 0.9829
## 8 -1.0633 0.0000 NaN
## 9 0.5186 210.7040 0.6147
## 10 0.5153 205.0437 0.7837
## 11 -0.1409 -56.6808 0.3783
## 12 -0.7431 -2.3458 1.0000
## 13 0.5142 203.1521 0.9855
## 14 -1.0633 0.0000 NaN
## 15 -0.2510 -24.9172 0.1985
## 16 -0.5522 -5.6219 1.0000
## 17 -0.7431 -2.3458 1.0000
## 18 -0.7431 -2.3458 1.0000
## 19 -0.7431 -2.3458 1.0000
## 20 0.5138 202.5209 0.8626
## 21 -1.0633 0.0000 NaN
## 22 -0.4219 -10.1102 1.0000
## 23 -1.0633 0.0000 NaN
## 24 0.5118 199.3611 1.0000
## 25 0.5114 198.7283 0.9044
## 26 0.5106 197.4618 0.9530
## 27 0.5102 196.8282 0.9647
## 28 -1.0633 0.0000 NaN
## 29 0.5098 196.1942 0.9537
## 30 -1.0633 0.0000 NaN
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 24.0000 11.0000 5.0000 2.0000 5.0000 21 5.0
## Value_Index 16.3929 94.1712 116.8642 -16.6876 180.4541 5467935 768709.4
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 5.0000 10.0000 11.000 3.0000 2.0000 2.0000 2.0000
## Value_Index 598.7869 2.8529 -0.854 0.1578 0.1428 0.8432 0.8857
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 2.0000 2.0000 5.0000 3.0000 11.0000 2.0000 2.0000
## Value_Index 30.5908 0.1285 0.2825 495.3075 0.8001 45.1353 0.0011
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 2.0000 0 5.0000 0 30.0000
## Value_Index 0.3393 0 1.4509 0 0.0046
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 1 1 1 1 1 1 1 1 1 1
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 1 1 1 1 1 1 1 1 1 1 1
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 1 1 1 1 1 1 1 1 1 1 1
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 1 1 1 1 1 1 1 1 1 1 1
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 1 1 1 1 1 1 1 1 1 1 1
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 1 1 1 1 1 1 1 1 1 1 1
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 1 1 1 1 1 1 1 1 1 1 1
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 1 1 1 1 1 1 1 1 1 1 1
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 1 1 1 1 1 1 1 1 1 1 1
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 1 1 1 1 1 1 1 1 1 1 1
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 1 1 1 1 1 1 1 1 1 1 1
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 1 1 1 2 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 1 1 1 1 1 1 1 1 1 1 1
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 1 1 1 1 1 1 1 1 1 1 1
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 1 1 1 1 1 1 1 1 1 1 1
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 1 1 1 1 1 1 1 1 1 1 1
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 1 1 1 1 1 1 1 1 1 1 1
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 1 1 1 1 1 1 1 1 1 1 1
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 1 1 1 1 1 1 1 1 1 1 1
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 1 1 1 1 1 1 1 1 1 1 1
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 1 1 1 1 1 1 1 1 1 1 1
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 1 1 1 1 1 1 1 1 1testH.nbclust_complete <- NbClust(data_aseg_pca$x[,1:2], distance="euclidean", min.nc=2, max.nc=30, method="complete", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 5 proposed 2 as the best number of clusters
## * 4 proposed 3 as the best number of clusters
## * 5 proposed 4 as the best number of clusters
## * 2 proposed 8 as the best number of clusters
## * 1 proposed 11 as the best number of clusters
## * 1 proposed 20 as the best number of clusters
## * 2 proposed 21 as the best number of clusters
## * 2 proposed 27 as the best number of clusters
## * 2 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_complete## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW
## 2 0.1989 274.4417 19.7750 -6.6822 239.8246 1020102.0 849235.5138
## 3 0.9426 157.8438 211.1326 -11.6034 287.6048 1880896.2 788052.4939
## 4 4.2695 268.2141 32.6857 -9.0530 503.5821 1359622.6 129459.3632
## 5 0.6644 236.1874 13.6221 -10.5361 591.8383 1470731.6 129520.0713
## 6 0.9375 201.7648 8.3957 -12.6204 657.5118 1610852.4 123994.5743
## 7 0.3194 174.8190 177.2944 -14.5835 673.2606 2053293.7 118730.2758
## 8 2487.9275 287.9514 29.0567 -7.2817 881.9286 1124184.6 42898.2387
## 9 0.0040 285.9082 12.5732 -7.3614 950.5895 1068800.2 38179.3658
## 10 0.8821 268.2042 9.1683 -8.3223 973.5467 1199138.0 33307.5680
## 11 0.1514 250.8274 161.9481 -9.3446 988.5472 1363045.1 30723.4962
## 12 22.2203 402.2417 12.8759 -2.1437 1183.3142 720517.6 6197.7760
## 13 1.3800 388.9043 21.9340 -2.6951 1208.1163 762584.6 5059.2619
## 14 0.6870 393.6216 9.8615 -2.5446 1260.7643 710211.4 4817.7498
## 15 0.2734 380.4681 40.1590 -3.1126 1287.0393 730748.5 4544.6490
## 16 3.8962 419.2894 7.7642 -1.6543 1410.9406 496156.1 4459.7082
## 17 2.6336 405.3762 15.4903 -2.2283 1443.7826 488479.9 4437.8187
## 18 0.5995 407.1103 8.4700 -2.2161 1465.1080 501076.8 3736.6632
## 19 1.0855 397.8331 8.1511 -2.6297 1483.1843 517793.2 3566.9966
## 20 0.0394 389.4542 152.5336 -3.0180 1497.0477 541529.9 3329.4556
## 21 130.7167 631.2467 9.3582 4.4336 1692.9535 263935.4 648.4558
## 22 0.8950 624.4581 11.1034 4.1992 1714.1940 265135.9 647.9933
## 23 0.3311 624.0623 5.9066 4.1226 1735.4227 265255.4 544.4748
## 24 1.0575 610.6072 5.7329 3.7148 1747.2608 274921.8 529.8921
## 25 1.8365 598.1529 6.8460 3.3248 1759.0946 283957.1 480.0016
## 26 1.1358 590.0279 6.7065 3.0421 1775.0305 287397.2 480.2233
## 27 0.0648 582.6365 34.0211 2.7754 1789.1484 292224.1 467.2758
## 28 22.6908 648.8708 8.7222 4.3808 1878.6595 216435.7 460.9246
## 29 0.2697 648.6768 11.6020 4.3035 1897.2639 214853.8 407.4621
## 30 639.2639 658.0133 6.9933 4.4528 1929.2312 201253.2 362.1275
## TraceW Friedman Rubin Cindex DB Silhouette Duda Pseudot2
## 2 1352.9393 1.5632 2.1531 0.1752 0.4914 0.7968 0.3849 11.1864
## 3 1249.1497 1.9729 2.3320 0.2207 0.5984 0.7612 0.5030 226.2487
## 4 660.6270 4.9554 4.4095 0.2119 0.7317 0.6620 0.4715 20.1744
## 5 580.2616 6.0099 5.0202 0.2613 0.8005 0.6259 0.3081 11.2279
## 6 548.4688 6.6517 5.3112 0.2632 0.6979 0.6307 12.7844 0.0000
## 7 529.4719 7.0127 5.5018 0.2855 0.5816 0.6362 0.4842 222.5968
## 8 300.6791 15.8875 9.6882 0.2439 0.6214 0.5923 0.3429 21.0806
## 9 267.2122 20.6589 10.9016 0.2611 0.6226 0.5986 0.7157 1.9864
## 10 253.4188 20.9896 11.4949 0.2902 0.5701 0.6002 0.2429 9.3502
## 11 243.7042 22.2186 11.9532 0.3109 0.5472 0.6015 0.4706 210.3940
## 12 142.7511 36.4906 20.4064 0.2360 0.6069 0.5145 0.2582 14.3638
## 13 135.1204 38.2054 21.5588 0.2666 0.6015 0.5098 0.5067 19.4684
## 14 123.2147 40.1456 23.6420 0.2700 0.6425 0.5058 0.2821 10.1782
## 15 118.0630 40.8154 24.6736 0.2796 0.6137 0.5081 0.4554 46.6299
## 16 100.1821 49.0049 29.0774 0.3132 0.5970 0.5072 0.3212 6.3387
## 17 96.8259 51.7696 30.0853 0.3292 0.5976 0.5075 0.5331 26.2700
## 18 90.5369 54.9032 32.1751 0.3373 0.6023 0.4792 0.3552 12.7057
## 19 87.2096 58.4979 33.4027 0.3505 0.5999 0.4765 0.5612 8.5992
## 20 84.1075 61.4939 34.6347 0.3562 0.5931 0.4794 0.3947 223.9187
## 21 49.6697 101.8354 58.6481 0.2123 0.6307 0.4830 41.7462 0.0000
## 22 47.6343 106.2350 61.1542 0.2236 0.5941 0.4895 16.0106 -0.9375
## 23 45.3257 113.1391 64.2690 0.2411 0.5514 0.4924 11.1639 -1.8209
## 24 44.1246 117.7337 66.0184 0.2610 0.5324 0.4948 14.8400 -0.9326
## 25 42.9838 121.3795 67.7706 0.2621 0.5003 0.4971 105.5903 0.0000
## 26 41.6574 124.9363 69.9285 0.2682 0.4756 0.5009 43.2375 0.0000
## 27 40.3915 130.9862 72.1199 0.2801 0.4491 0.5060 0.4848 46.7623
## 28 34.8286 150.2423 83.6392 0.2721 0.4505 0.5048 0.5938 6.1559
## 29 33.4523 152.7262 87.0803 0.2792 0.4831 0.5034 0.7443 8.9311
## 30 31.7088 155.6101 91.8685 0.2788 0.5435 0.4913 0.2650 8.3195
## Beale Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex
## 2 1.3983 0.3478 676.4696 0.7761 10.8815 0.0135 0.2154 7e-04 6.4732
## 3 0.9837 0.3166 416.3832 0.7763 6.9241 0.0136 0.2717 8e-04 4.3673
## 4 1.0618 0.3695 165.1568 0.7687 4.5640 0.0534 0.1003 7e-04 3.9731
## 5 1.8713 0.3596 116.0523 0.7678 3.7196 0.0543 0.1246 7e-04 3.4523
## 6 0.0000 0.3451 91.4115 0.7678 1.8488 0.0544 0.1256 7e-04 2.7340
## 7 1.0600 0.3209 75.6388 0.7678 4.4362 0.0544 0.1362 7e-04 1.6137
## 8 1.7567 0.3085 37.5849 0.6936 2.2659 0.1040 0.0910 7e-04 1.6666
## 9 0.3311 0.2927 29.6902 0.6933 2.5474 0.1043 0.0979 7e-04 1.6525
## 10 2.3375 0.2812 25.3419 0.6932 3.6607 0.1044 0.1089 7e-04 1.6552
## 11 1.1191 0.2685 22.1549 0.6931 4.1658 0.1045 0.1167 7e-04 1.5455
## 12 2.3940 0.2673 11.8959 0.5410 1.0648 0.2175 0.0632 7e-04 2.1204
## 13 0.9271 0.2581 10.3939 0.5409 2.2696 0.2175 0.0715 7e-04 2.0932
## 14 2.0356 0.2518 8.8010 0.5385 1.4936 0.2193 0.0734 7e-04 2.4576
## 15 1.1657 0.2447 7.8709 0.5384 2.2597 0.2194 0.0760 7e-04 2.4860
## 16 1.5847 0.2408 6.2614 0.5325 1.9075 0.2240 0.0879 7e-04 2.4826
## 17 0.8474 0.2344 5.6956 0.5324 3.3585 0.2240 0.0925 7e-04 2.5217
## 18 1.5882 0.2280 5.0298 0.5295 3.9383 0.2267 0.0957 7e-04 2.8176
## 19 0.7166 0.2220 4.5900 0.5290 2.7645 0.2272 0.0995 7e-04 3.1244
## 20 1.5233 0.2165 4.2054 0.5284 2.6734 0.2277 0.1014 7e-04 3.2195
## 21 0.0000 0.2132 2.3652 0.4022 0.3841 0.3492 0.0460 7e-04 3.8474
## 22 -0.4688 0.2086 2.1652 0.4022 0.4466 0.3491 0.0485 7e-04 3.8474
## 23 -0.6070 0.2041 1.9707 0.4022 0.9672 0.3489 0.0524 7e-04 3.7294
## 24 -0.4663 0.1998 1.8385 0.4021 0.9155 0.3488 0.0567 7e-04 3.8119
## 25 0.0000 0.1959 1.7194 0.4021 0.6055 0.3488 0.0570 7e-04 3.8889
## 26 0.0000 0.1922 1.6022 0.4021 0.6347 0.3487 0.0584 7e-04 3.8000
## 27 1.0392 0.1887 1.4960 0.4021 1.6437 0.3486 0.0610 7e-04 3.7989
## 28 0.6156 0.1861 1.2439 0.3929 1.7568 0.3522 0.0634 7e-04 4.3980
## 29 0.3308 0.1830 1.1535 0.3921 2.7272 0.3526 0.0654 7e-04 5.3258
## 30 2.0799 0.1802 1.0570 0.3863 1.4326 0.3594 0.0669 7e-04 7.5270
## Dindex SDbw
## 2 1.8034 0.8774
## 3 1.7696 0.5583
## 4 1.3615 0.5502
## 5 1.2996 0.6952
## 6 1.2660 0.4876
## 7 1.2403 0.1356
## 8 0.9620 0.1156
## 9 0.9143 0.0895
## 10 0.8971 0.0747
## 11 0.8821 0.0543
## 12 0.6777 0.0523
## 13 0.6631 0.0469
## 14 0.6366 0.0442
## 15 0.6234 0.0390
## 16 0.5781 0.0445
## 17 0.5682 0.0405
## 18 0.5491 0.0442
## 19 0.5389 0.0400
## 20 0.5315 0.0315
## 21 0.3936 0.0300
## 22 0.3851 0.0196
## 23 0.3767 0.0160
## 24 0.3725 0.0145
## 25 0.3677 0.0124
## 26 0.3609 0.0103
## 27 0.3543 0.0080
## 28 0.3304 0.0084
## 29 0.3246 0.0082
## 30 0.3165 0.0082
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 -0.1409 -56.6808 0.2795
## 3 0.5193 211.9589 0.3747
## 4 0.1299 120.5893 0.3564
## 5 -0.2510 -24.9172 0.2040
## 6 -1.0633 0.0000 NaN
## 7 0.5118 199.3611 0.3474
## 8 -0.0027 -4016.9908 0.1960
## 9 -0.2510 -24.9172 0.7257
## 10 -0.4219 -10.1102 0.1776
## 11 0.5022 185.3717 0.3277
## 12 -0.2510 -24.9172 0.1414
## 13 0.1556 108.5678 0.4040
## 14 -0.3258 -16.2785 0.1929
## 15 0.2963 92.6281 0.3171
## 16 -0.4219 -10.1102 0.2802
## 17 0.2454 92.2265 0.4336
## 18 -0.1409 -56.6808 0.2390
## 19 -0.0027 -4016.9908 0.4995
## 20 0.4788 158.9030 0.2197
## 21 -1.0633 0.0000 NaN
## 22 -0.7431 -2.3458 1.0000
## 23 -0.5522 -5.6219 1.0000
## 24 -0.7431 -2.3458 1.0000
## 25 -1.0633 0.0000 NaN
## 26 -1.0633 0.0000 NaN
## 27 0.3178 94.4356 0.3581
## 28 -0.0624 -153.2995 0.5513
## 29 0.2153 94.7474 0.7199
## 30 -0.4219 -10.1102 0.2060
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 8.000 30.0000 3.0000 30.0000 4.0000 8.0 4.0
## Value_Index 2487.927 658.0133 191.3576 4.4528 215.9773 873724.8 658593.1
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 4.0000 21.0000 21.0000 2.0000 27.0000 2.0000 2.0000
## Value_Index 508.1573 40.3415 -21.5073 0.1752 0.4491 0.7968 0.3849
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 4.0000 2.0000 4.0000 3.0000 3.0000 20.0000 2.0000
## Value_Index 20.1744 1.3983 0.3695 260.0864 0.7763 2.6734 0.0135
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 3.0000 0 11.0000 0 27.000
## Value_Index 0.2717 0 1.5455 0 0.008
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 2 2 2 2 2 2 2 2 2 2
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 2 2 2 2 2 2 2 2 2 2 2
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 2 2 2 2 2 2 2 2 2 2 2
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 2 2 2 2 2 2 2 2 2 2 2
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 2 2 2 2 2 2 2 2 2 2 2
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 2 2 2 2 2 2 2 2 2 2 2
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 2 2 2 2 2 2 2 2 2 2 2
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 2 2 2 2 2 2 2 2 2 2 2
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 2 2 2 2 2 2 2 2 2 2 2
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 2 2 2 2 2 2 2 2 2 2 2
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 2 2 2 2 2 2 2 2 2 2 2
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 2 2 2 1 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 2 2 2 2 2 2 2 2 2 2 2
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 2 2 2 2 2 2 2 2 2 2 2
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 2 2 2 2 2 2 2 2 2 2 2
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 2 2 2 2 2 2 2 2 2 2 2
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 2 2 2 2 2 2 2 2 2 2 2
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 2 2 2 2 2 2 2 2 2 2 2
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 2 2 2 2 2 2 2 2 2 2 2
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 2 2 2 2 2 2 2 2 2 2 2
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 2 2 2 2 2 2 2 2 2 2 2
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 2 2 2 2 2 2 2 2 2testH.nbclust_Average <- NbClust(data_aseg_pca$x[,1:2], distance="euclidean", min.nc=2, max.nc=30, method="average", index="all")## [1] "Frey index : No clustering structure in this data set"
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 6 proposed 2 as the best number of clusters
## * 3 proposed 3 as the best number of clusters
## * 3 proposed 4 as the best number of clusters
## * 2 proposed 6 as the best number of clusters
## * 3 proposed 8 as the best number of clusters
## * 2 proposed 18 as the best number of clusters
## * 2 proposed 22 as the best number of clusters
## * 1 proposed 26 as the best number of clusters
## * 1 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_Average## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 0.1968 274.4417 19.0073 -6.6822 239.8246 1020102.0 849235.514 1352.9393
## 3 1.0056 157.0207 201.0029 -11.6452 283.8989 1910165.5 786561.215 1252.8812
## 4 2.0903 259.3634 13.0075 -9.5315 474.6847 1533592.5 179863.113 677.9243
## 5 0.9488 207.6124 7.2030 -12.3498 520.7486 1977764.9 173780.675 642.5113
## 6 1.4956 171.8868 15.4608 -14.8420 533.0420 2705773.2 165763.068 623.4032
## 7 0.2012 154.6163 232.9312 -16.2760 597.5634 2814683.6 164248.054 584.7666
## 8 8.0446 297.0131 6.7491 -6.8138 845.9589 1305950.8 31122.577 292.4265
## 9 1.3655 267.1340 42.7586 -8.3848 857.4217 1575757.0 28343.635 284.1600
## 10 1.2458 284.9175 10.1628 -7.4088 961.2429 1262215.7 23380.849 239.7768
## 11 1.0090 267.6039 8.8570 -8.3691 977.1481 1429346.4 20922.707 229.6303
## 12 0.7323 252.3837 3.8412 -9.2779 1005.0656 1514245.7 20711.655 221.0797
## 13 0.9943 234.5363 3.2498 -10.4173 1014.0436 1711883.6 19881.410 217.4168
## 14 1.8665 218.8760 23.9272 -11.4983 1019.0729 1944208.6 19155.009 214.3481
## 15 0.6670 225.4668 3.9646 -11.1024 1105.5067 1556904.9 19026.385 193.8271
## 16 0.8837 213.4550 2.2290 -11.9789 1123.1702 1645721.3 18959.071 190.4709
## 17 0.1139 201.3418 194.3585 -12.9136 1127.5957 1823921.2 18658.022 188.5943
## 18 18.4246 364.4489 2.9612 -3.9281 1354.6107 794064.6 3569.371 100.7683
## 19 0.2232 347.3856 62.4077 -4.7243 1362.4984 856139.8 3569.046 99.4419
## 20 14.5874 423.3967 14.5089 -1.7238 1521.6369 488795.1 2758.265 77.5443
## 21 1.3338 427.5268 13.0715 -1.6344 1558.2267 462694.1 2602.950 72.7467
## 22 0.4102 430.1205 3.6840 -1.6035 1586.9721 450488.9 2390.873 68.6492
## 23 1.0963 415.7594 3.9306 -2.1941 1592.5085 481145.0 2283.375 67.5084
## 24 0.9662 403.1905 3.4783 -2.7351 1604.2470 498886.1 2253.453 66.3073
## 25 0.3707 390.9396 24.4529 -3.2793 1615.0312 517540.4 2227.964 65.2565
## 26 3.4540 417.0162 3.7609 -2.3481 1686.3967 415786.8 2000.674 58.5925
## 27 0.9753 406.2614 3.4254 -2.8217 1693.1250 435989.8 1917.301 57.5806
## 28 0.8327 395.7661 2.3694 -3.2966 1704.1847 447766.6 1874.789 56.6692
## 29 4.2064 384.1608 8.5122 -3.8276 1707.6795 473377.5 1821.063 56.0429
## 30 2.1083 384.3407 6.4186 -3.8920 1749.7744 425089.9 1807.399 53.8697
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale
## 2 1.5632 2.1531 0.1752 0.4914 0.7968 1.3159 -1.6803 -0.2100
## 3 1.9460 2.3251 0.2208 0.3740 0.7779 0.5145 216.1118 0.9396
## 4 5.2071 4.2970 0.2246 0.6076 0.6917 0.4844 6.3872 0.9125
## 5 5.5470 4.5338 0.2570 0.5437 0.6928 3.2042 -2.7516 -0.5503
## 6 5.8579 4.6728 0.2586 0.4604 0.6951 0.4194 16.6144 1.2780
## 7 6.6034 4.9815 0.2581 0.5351 0.6754 0.4613 251.0484 1.1623
## 8 17.7832 9.9616 0.1814 0.6098 0.6059 3.6137 -2.8931 -0.5786
## 9 18.3330 10.2514 0.1813 0.5494 0.6033 0.4896 31.2743 1.0088
## 10 20.0502 12.1489 0.2755 0.5311 0.5962 0.2093 11.3367 2.8342
## 11 21.2256 12.6858 0.2910 0.4727 0.6012 0.4181 8.3501 1.1929
## 12 22.1735 13.1764 0.2907 0.5049 0.6020 4.9738 -3.1958 -0.6392
## 13 22.3014 13.3984 0.2906 0.4786 0.5944 9.1521 -2.6722 -0.6681
## 14 22.6819 13.5902 0.2906 0.4389 0.5989 0.4531 28.9701 1.1588
## 15 26.9072 15.0290 0.3569 0.4855 0.5611 0.3212 6.3387 1.5847
## 16 27.8593 15.2939 0.3568 0.4927 0.5615 16.1084 -0.9379 -0.4690
## 17 28.3358 15.4460 0.3568 0.4590 0.5626 0.4625 212.6540 1.1557
## 18 57.4219 28.9082 0.2501 0.5024 0.5015 105.5903 0.0000 0.0000
## 19 58.5163 29.2939 0.2501 0.4714 0.5053 0.4413 64.5735 1.2418
## 20 68.4175 37.5661 0.2493 0.4843 0.5151 0.4708 12.3641 1.0303
## 21 77.9222 40.0435 0.2479 0.5055 0.5075 0.4836 11.7466 0.9789
## 22 86.8942 42.4336 0.3449 0.5134 0.5072 14.8400 -0.9326 -0.4663
## 23 87.7972 43.1507 0.3448 0.4864 0.5088 11.1639 -1.8209 -0.6070
## 24 91.6009 43.9323 0.3466 0.4610 0.5112 23.2289 -0.9570 -0.4785
## 25 95.2597 44.6398 0.3466 0.4452 0.5133 0.3638 40.2140 1.6756
## 26 125.2129 49.7168 0.3627 0.4474 0.4613 10.5721 -2.7162 -0.6791
## 27 125.5077 50.5906 0.3625 0.4349 0.4629 2.9515 -1.9836 -0.4959
## 28 127.3175 51.4042 0.3624 0.4229 0.4629 85.4573 0.0000 0.0000
## 29 127.8024 51.9787 0.3624 0.3911 0.4686 0.2823 17.8000 2.2250
## 30 142.5682 54.0756 0.3618 0.3886 0.4677 0.3715 10.1499 1.4500
## Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex
## 2 0.3478 676.4696 0.7761 4.3720 0.0135 0.2154 7e-04 3.4730 1.8034
## 3 0.3132 417.6271 0.7769 6.6824 0.0135 0.2717 8e-04 1.4485 1.7616
## 4 0.3282 169.4811 0.8036 5.6050 0.0396 0.2027 7e-04 1.4366 1.3704
## 5 0.3250 128.5023 0.8034 7.2189 0.0397 0.2322 7e-04 1.3561 1.3386
## 6 0.2977 103.9005 0.8033 14.0111 0.0398 0.2338 7e-04 1.0926 1.3191
## 7 0.2966 83.5381 0.8010 5.0972 0.0404 0.1633 7e-04 1.2421 1.2819
## 8 0.2931 36.5533 0.6822 2.3576 0.1112 0.0624 7e-04 1.2545 0.9392
## 9 0.2778 31.5733 0.6822 2.4926 0.1113 0.0624 7e-04 1.2821 0.9256
## 10 0.2813 23.9777 0.6804 2.8911 0.1128 0.0963 7e-04 1.2663 0.8742
## 11 0.2687 20.8755 0.6803 4.8525 0.1129 0.1018 7e-04 1.2507 0.8568
## 12 0.2598 18.4233 0.6799 6.5827 0.1131 0.1018 7e-04 1.6582 0.8383
## 13 0.2506 16.7244 0.6798 7.3641 0.1132 0.1018 7e-04 1.6535 0.8283
## 14 0.2416 15.3106 0.6797 7.5383 0.1133 0.1018 7e-04 1.8121 0.8205
## 15 0.2382 12.9218 0.6741 9.6036 0.1164 0.1249 7e-04 1.9941 0.7812
## 16 0.2314 11.9044 0.6739 11.0031 0.1165 0.1249 7e-04 2.1614 0.7713
## 17 0.2246 11.0938 0.6738 4.0784 0.1165 0.1249 7e-04 2.1508 0.7653
## 18 0.2227 5.5982 0.4927 1.6983 0.2677 0.0627 7e-04 2.3433 0.5657
## 19 0.2169 5.2338 0.4927 2.0086 0.2677 0.0627 7e-04 2.3219 0.5589
## 20 0.2165 3.8772 0.4773 1.8208 0.2802 0.0682 7e-04 2.7056 0.4997
## 21 0.2114 3.4641 0.4764 2.1437 0.2808 0.0682 7e-04 2.8302 0.4871
## 22 0.2066 3.1204 0.4756 2.1401 0.2815 0.0954 7e-04 2.9526 0.4774
## 23 0.2022 2.9351 0.4755 2.2774 0.2816 0.0954 7e-04 3.0287 0.4727
## 24 0.1980 2.7628 0.4755 2.4040 0.2816 0.0959 7e-04 3.0999 0.4684
## 25 0.1940 2.6103 0.4754 2.7574 0.2817 0.0959 7e-04 3.1291 0.4644
## 26 0.1904 2.2536 0.4716 2.8990 0.2856 0.1018 7e-04 3.5287 0.4398
## 27 0.1870 2.1326 0.4715 2.9991 0.2857 0.1018 7e-04 3.5556 0.4346
## 28 0.1838 2.0239 0.4714 3.0374 0.2858 0.1018 7e-04 3.6523 0.4307
## 29 0.1807 1.9325 0.4714 3.6278 0.2859 0.1018 7e-04 3.6262 0.4260
## 30 0.1780 1.7957 0.4708 4.1667 0.2865 0.1018 7e-04 3.9493 0.4156
## SDbw
## 2 0.8774
## 3 0.6590
## 4 0.3319
## 5 0.2129
## 6 0.1335
## 7 0.0989
## 8 0.1013
## 9 0.0819
## 10 0.0731
## 11 0.0523
## 12 0.0457
## 13 0.0446
## 14 0.0304
## 15 0.0375
## 16 0.0409
## 17 0.0348
## 18 0.0243
## 19 0.0220
## 20 0.0204
## 21 0.0191
## 22 0.0179
## 23 0.0161
## 24 0.0145
## 25 0.0094
## 26 0.0088
## 27 0.0080
## 28 0.0074
## 29 0.0064
## 30 0.0058
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 -0.1409 -56.6808 1.0000
## 3 0.5193 211.9589 0.3915
## 4 -0.1908 -37.4469 0.4277
## 5 -0.3258 -16.2785 1.0000
## 6 0.0222 529.7343 0.2969
## 7 0.5142 203.1521 0.3138
## 8 -0.3258 -16.2785 1.0000
## 9 0.2454 92.2265 0.3707
## 10 -0.4219 -10.1102 0.1360
## 11 -0.1908 -37.4469 0.3369
## 12 -0.3258 -16.2785 1.0000
## 13 -0.4219 -10.1102 1.0000
## 14 0.1977 97.3833 0.3225
## 15 -0.4219 -10.1102 0.2802
## 16 -0.7431 -2.3458 1.0000
## 17 0.5003 182.8126 0.3160
## 18 -1.0633 0.0000 NaN
## 19 0.3427 97.8113 0.2932
## 20 -0.0027 -4016.9908 0.3735
## 21 -0.0027 -4016.9908 0.3915
## 22 -0.7431 -2.3458 1.0000
## 23 -0.5522 -5.6219 1.0000
## 24 -0.7431 -2.3458 1.0000
## 25 0.1881 99.2518 0.1984
## 26 -0.4219 -10.1102 1.0000
## 27 -0.4219 -10.1102 1.0000
## 28 -1.0633 0.0000 NaN
## 29 -0.1409 -56.6808 0.1449
## 30 -0.1908 -37.4469 0.2729
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 18.0000 22.0000 8.0000 22.0000 8.0000 8 4.0
## Value_Index 18.4246 430.1205 226.1821 -1.6035 248.3955 1778539 606698.1
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 4.0000 26.0000 18.0000 2.0000 3.000 2.0000 2.0000
## Value_Index 539.5438 29.9532 -13.0766 0.1752 0.374 0.7968 1.3159
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 6.0000 2.00 2.0000 3.0000 4.0000 NA 2.0000
## Value_Index 16.6144 -0.21 0.3478 258.8426 0.8036 NA 0.0135
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 3.0000 0 6.0000 0 30.0000
## Value_Index 0.2717 0 1.0926 0 0.0058
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 2 2 2 2 2 2 2 2 2 2
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 2 2 2 2 2 2 2 2 2 2 2
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 2 2 2 2 2 2 2 2 2 2 2
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 2 2 2 2 2 2 2 2 2 2 2
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 2 2 2 2 2 2 2 2 2 2 2
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 2 2 2 2 2 2 2 2 2 2 2
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 2 2 2 2 2 2 2 2 2 2 2
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 2 2 2 2 2 2 2 2 2 2 2
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 2 2 2 2 2 2 2 2 2 2 2
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 2 2 2 2 2 2 2 2 2 2 2
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 2 2 2 2 2 2 2 2 2 2 2
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 2 2 2 1 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 2 2 2 2 2 2 2 2 2 2 2
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 2 2 2 2 2 2 2 2 2 2 2
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 2 2 2 2 2 2 2 2 2 2 2
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 2 2 2 2 2 2 2 2 2 2 2
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 2 2 2 2 2 2 2 2 2 2 2
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 2 2 2 2 2 2 2 2 2 2 2
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 2 2 2 2 2 2 2 2 2 2 2
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 2 2 2 2 2 2 2 2 2 2 2
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 2 2 2 2 2 2 2 2 2 2 2
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 2 2 2 2 2 2 2 2 2testH.nbclust_ward <- NbClust(data_aseg_pca$x[,1:2], distance="euclidean", min.nc=2, max.nc=30, method="ward.D2", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 5 proposed 2 as the best number of clusters
## * 5 proposed 3 as the best number of clusters
## * 5 proposed 4 as the best number of clusters
## * 1 proposed 6 as the best number of clusters
## * 1 proposed 9 as the best number of clusters
## * 1 proposed 11 as the best number of clusters
## * 1 proposed 12 as the best number of clusters
## * 1 proposed 27 as the best number of clusters
## * 1 proposed 29 as the best number of clusters
## * 3 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_ward## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 5.1126 394.2464 97.4622 -3.0642 281.8735 856157.21 325460.6253 1096.5701
## 3 0.3975 325.2050 135.5389 -4.9574 411.8507 1120816.12 206645.2458 777.9825
## 4 66.1171 384.3429 59.8005 -3.7062 593.7157 933934.17 45772.8915 494.9332
## 5 0.0308 374.6551 74.2538 -3.6856 690.8346 973629.52 36645.6607 394.8751
## 6 3.2412 407.5380 47.3904 -2.1576 849.2645 724548.86 21913.9141 300.0631
## 7 1.5894 414.5143 38.5365 -1.7654 919.7744 735138.78 15445.8636 249.5279
## 8 0.3357 417.7662 45.2860 -1.5731 985.3506 730616.20 11905.9794 214.1149
## 9 1.4389 440.6524 37.3019 -0.7072 1074.2321 638495.47 9077.9256 179.1459
## 10 0.5906 457.0987 44.0324 -0.1256 1144.6973 587708.28 5053.4029 154.2393
## 11 0.8607 492.4003 47.5260 1.0298 1247.7802 462820.26 3721.6416 129.4556
## 12 1.9453 542.4792 33.3643 2.5266 1327.1991 395618.19 2066.6447 107.2063
## 13 1.1097 570.3088 30.9811 3.2791 1384.3966 365845.90 1808.5203 93.5210
## 14 1.8100 598.0246 23.7744 3.9835 1448.3096 325097.10 1701.8688 82.2900
## 15 0.9355 612.7001 23.3674 4.3171 1507.6806 291409.72 1567.4002 74.4573
## 16 0.8209 629.9888 24.5564 4.7022 1551.0297 276769.79 1421.9014 67.4521
## 17 0.8780 653.9637 25.6803 5.2328 1597.5660 257375.02 1232.1655 60.7881
## 18 0.8115 684.8006 28.7757 5.8969 1647.6910 234158.20 842.6328 54.5107
## 19 1.3488 728.8892 24.3975 6.8141 1704.5326 205879.59 523.6842 48.2558
## 20 1.4254 764.5668 20.2494 7.4995 1750.4778 188375.94 465.3844 43.4582
## 21 0.9830 790.5950 20.1705 7.9582 1796.8272 171211.11 341.2341 39.7953
## 22 1.2739 819.4976 17.7679 8.4530 1843.8563 154467.37 327.9413 36.4392
## 23 1.3602 842.9272 15.3244 8.8253 1878.8799 145904.84 313.8831 33.6931
## 24 1.0118 859.9023 14.9367 9.0668 1909.0507 140100.83 244.7565 31.4706
## 25 0.9004 877.5994 15.3502 9.3140 1942.1836 132416.55 244.5250 29.4351
## 26 0.9296 899.0594 15.6898 9.6194 1973.1230 125898.95 221.7340 27.4736
## 27 1.2121 924.1260 14.1798 9.9760 2005.9531 118411.81 194.8258 25.5969
## 28 1.3228 945.2078 12.4028 10.2543 2035.8910 112411.08 156.3931 23.9993
## 29 0.9453 960.6637 12.4780 10.4327 2065.5055 106585.90 156.3964 22.6728
## 30 0.9179 978.1617 12.7843 10.6389 2097.7616 99718.77 156.3033 21.4069
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale
## 2 2.2068 2.6565 0.0911 0.6943 0.7611 0.4248 28.4357 1.2925
## 3 4.0161 3.7443 0.1311 0.7588 0.6882 0.4784 234.3723 1.0851
## 4 8.7187 5.8857 0.0768 0.8854 0.4925 1.3159 -1.6803 -0.2100
## 5 12.8001 7.3771 0.1310 0.7391 0.4970 0.5753 61.2619 0.7293
## 6 25.3827 9.7081 0.0975 0.8880 0.4739 0.3661 45.0129 1.6671
## 7 25.9801 11.6742 0.0934 0.7500 0.4910 0.4844 6.3872 0.9125
## 8 26.6738 13.6050 0.1062 0.7118 0.4933 0.4745 13.2905 1.0223
## 9 27.8481 16.2607 0.1044 0.7138 0.4964 0.3155 282.0429 2.1530
## 10 33.9375 18.8865 0.0854 0.7445 0.4512 0.4914 56.9232 1.0165
## 11 36.0356 22.5022 0.0651 0.7232 0.4922 0.3034 9.1842 1.8368
## 12 48.6111 27.1722 0.0793 0.6961 0.4952 0.4861 7.4012 0.9251
## 13 58.8411 31.1485 0.1246 0.6839 0.4972 0.5347 17.4050 0.8288
## 14 61.8379 35.3996 0.1165 0.7300 0.4905 0.2819 12.7343 2.1224
## 15 64.2855 39.1236 0.1152 0.7057 0.4927 12.4791 -0.9199 -0.4599
## 16 74.0391 43.1868 0.1559 0.6380 0.4968 0.3638 40.2140 1.6756
## 17 87.7910 47.9212 0.1473 0.6366 0.4897 0.4275 84.3585 1.3181
## 18 93.8148 53.4397 0.1158 0.6354 0.4970 0.5357 26.0043 0.8388
## 19 108.1605 60.3665 0.0990 0.6687 0.5018 0.4708 12.3641 1.0303
## 20 126.8929 67.0308 0.0941 0.6792 0.5035 4.9738 -3.1958 -0.6392
## 21 133.2075 73.2005 0.1024 0.6559 0.5071 0.3212 6.3387 1.5847
## 22 137.7178 79.9424 0.1113 0.6537 0.5078 0.4162 30.8602 1.3417
## 23 152.0875 86.4581 0.1026 0.6514 0.5118 0.4212 9.6202 1.2025
## 24 166.0320 92.5637 0.1004 0.6433 0.5104 41.7462 0.0000 0.0000
## 25 177.4482 98.9646 0.1002 0.6096 0.5167 0.2192 21.3710 3.0530
## 26 198.6676 106.0303 0.0985 0.5889 0.5239 16.1084 -0.9379 -0.4690
## 27 225.0476 113.8041 0.1175 0.5642 0.5250 0.3715 10.1499 1.4500
## 28 231.6725 121.3802 0.1157 0.5626 0.5279 105.5903 0.0000 0.0000
## 29 245.8728 128.4814 0.1155 0.5403 0.5317 0.5470 27.3313 0.8039
## 30 262.3889 136.0795 0.1022 0.5602 0.5313 0.4722 15.6515 1.0434
## Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex
## 2 0.3214 548.2851 0.7951 1.1143 0.0390 0.0805 7e-04 9.7204 1.5709
## 3 0.3577 259.3275 0.8026 6.6768 0.0396 0.1182 7e-04 6.3281 1.4121
## 4 0.3481 123.7333 0.4935 -0.4630 0.2852 0.0126 7e-04 5.5625 1.0167
## 5 0.3252 78.9750 0.4946 0.6809 0.2836 0.0215 7e-04 3.2461 0.9750
## 6 0.3007 50.0105 0.4943 0.2784 0.2766 0.0215 7e-04 3.7235 0.8311
## 7 0.3096 35.6468 0.4960 -0.0909 0.2706 0.0215 7e-04 3.4418 0.7732
## 8 0.3063 26.7644 0.4966 0.1971 0.2691 0.0247 7e-04 3.0994 0.7414
## 9 0.3027 19.9051 0.4975 5.5429 0.2665 0.0247 7e-04 2.9770 0.7054
## 10 0.2904 15.4239 0.3603 0.5826 0.5459 0.0126 7e-04 4.6099 0.5648
## 11 0.2850 11.7687 0.3482 -0.0075 0.5049 0.0126 7e-04 4.6876 0.5036
## 12 0.2735 8.9339 0.3486 0.0539 0.4994 0.0155 7e-04 4.2723 0.4824
## 13 0.2636 7.1939 0.3489 0.3743 0.4929 0.0248 7e-04 4.3061 0.4681
## 14 0.2567 5.8779 0.3478 0.1814 0.4748 0.0248 7e-04 4.4313 0.4426
## 15 0.2500 4.9638 0.3478 0.0434 0.4711 0.0248 7e-04 4.4740 0.4242
## 16 0.2424 4.2158 0.3479 0.7300 0.4701 0.0336 7e-04 4.0885 0.4085
## 17 0.2354 3.5758 0.3447 1.6306 0.4616 0.0336 7e-04 4.3746 0.3839
## 18 0.2297 3.0284 0.3092 0.4479 0.4943 0.0336 8e-04 5.8798 0.3485
## 19 0.2241 2.5398 0.3051 0.2860 0.4495 0.0336 8e-04 6.0191 0.3309
## 20 0.2186 2.1729 0.3046 0.1253 0.4332 0.0336 8e-04 6.1843 0.3183
## 21 0.2140 1.8950 0.3046 0.1788 0.4295 0.0369 8e-04 6.2006 0.3083
## 22 0.2097 1.6563 0.3046 0.7275 0.4258 0.0405 8e-04 6.2532 0.2984
## 23 0.2053 1.4649 0.3010 0.4489 0.4087 0.0405 8e-04 6.3744 0.2849
## 24 0.2011 1.3113 0.3005 0.1295 0.4029 0.0405 8e-04 6.5510 0.2766
## 25 0.1972 1.1774 0.3005 0.4602 0.4021 0.0405 8e-04 6.5045 0.2682
## 26 0.1934 1.0567 0.3001 0.1818 0.3975 0.0405 8e-04 6.6241 0.2581
## 27 0.1899 0.9480 0.3001 0.4860 0.3962 0.0485 8e-04 6.4344 0.2520
## 28 0.1867 0.8571 0.2997 0.2017 0.3920 0.0485 8e-04 6.5617 0.2448
## 29 0.1836 0.7818 0.2997 1.5887 0.3914 0.0485 8e-04 6.3656 0.2381
## 30 0.1806 0.7136 0.2876 0.8137 0.3864 0.0485 8e-04 9.9723 0.2280
## SDbw
## 2 1.0724
## 3 0.7017
## 4 0.5998
## 5 0.2718
## 6 0.2466
## 7 0.1942
## 8 0.1640
## 9 0.1296
## 10 0.1237
## 11 0.1293
## 12 0.1005
## 13 0.0847
## 14 0.0876
## 15 0.0742
## 16 0.0531
## 17 0.0606
## 18 0.0662
## 19 0.0560
## 20 0.0513
## 21 0.0448
## 22 0.0367
## 23 0.0356
## 24 0.0284
## 25 0.0253
## 26 0.0203
## 27 0.0204
## 28 0.0191
## 29 0.0142
## 30 0.0136
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.1671 104.6547 0.2853
## 3 0.5142 203.1521 0.3388
## 4 -0.1409 -56.6808 1.0000
## 5 0.4140 117.4720 0.4838
## 6 0.2153 94.7474 0.1987
## 7 -0.1908 -37.4469 0.4277
## 8 0.0222 529.7343 0.3749
## 9 0.4669 148.4332 0.1182
## 10 0.3548 100.0055 0.3652
## 11 -0.3258 -16.2785 0.2206
## 12 -0.1409 -56.6808 0.4194
## 13 0.1556 108.5678 0.4439
## 14 -0.2510 -24.9172 0.1705
## 15 -0.7431 -2.3458 1.0000
## 16 0.1881 99.2518 0.1984
## 17 0.3756 104.7312 0.2713
## 18 0.2454 92.2265 0.4372
## 19 -0.0027 -4016.9908 0.3735
## 20 -0.3258 -16.2785 1.0000
## 21 -0.4219 -10.1102 0.2802
## 22 0.1780 101.6241 0.2719
## 23 -0.1409 -56.6808 0.3296
## 24 -1.0633 0.0000 NaN
## 25 -0.1908 -37.4469 0.0848
## 26 -0.7431 -2.3458 1.0000
## 27 -0.1908 -37.4469 0.2729
## 28 -1.0633 0.0000 NaN
## 29 0.2646 91.7349 0.4519
## 30 0.0647 202.2234 0.3655
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 4.0000 30.0000 4.0000 30.0000 4.0000 6.0 4.0
## Value_Index 66.1171 978.1617 75.7384 10.6389 181.8649 259670.6 160872.4
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 4.0000 27.00 12.0000 11.0000 29.0000 2.0000 2.0000
## Value_Index 182.9912 26.38 -0.6938 0.0651 0.5403 0.7611 0.4248
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 2.0000 2.0000 3.0000 3.0000 3.0000 3.0000 2.000
## Value_Index 28.4357 1.2925 0.3577 288.9576 0.8026 6.6768 0.039
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 3.0000 0 9.000 0 30.0000
## Value_Index 0.1182 0 2.977 0 0.0136
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 1 1 1 2 2 2 2 2 2 2
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 2 2 2 2 2 2 2 2 2 2 2
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 2 2 2 2 2 2 2 2 2 2 2
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 2 2 2 2 2 2 2 2 2 2 2
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 2 2 2 2 2 2 2 2 2 2 2
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 2 2 2 2 2 2 2 2 2 2 2
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 2 2 2 2 2 2 2 2 2 2 2
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 2 2 2 2 2 2 2 2 2 2 2
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 2 2 2 2 2 2 2 2 2 2 2
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 2 2 2 2 2 2 2 2 2 2 2
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 2 2 2 2 2 2 2 2 2 2 2
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 2 2 2 1 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 1 1 1 1 1 1 1 1 1 1 1
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 2 2 2 2 2 2 2 2 2 2 2
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 2 2 2 2 2 2 2 2 2 2 2
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 2 2 2 2 2 2 2 2 2 2 2
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 2 2 2 2 2 2 2 2 2 2 2
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 2 2 2 2 2 2 2 2 2 2 2
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 2 2 2 2 2 2 2 2 2 2 2
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 2 2 2 2 2 2 2 2 2 2 2
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 2 2 2 2 2 2 2 2 2 2 2
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 2 2 2 2 2 2 2 2 2# Distancia Manhattan y varios linkage
testH.nbclust_single_m <- NbClust(data_aseg_pca$x[,1:2], distance="manhattan", min.nc=2, max.nc=30, method="single", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 9 proposed 2 as the best number of clusters
## * 2 proposed 3 as the best number of clusters
## * 5 proposed 5 as the best number of clusters
## * 5 proposed 11 as the best number of clusters
## * 1 proposed 15 as the best number of clusters
## * 1 proposed 21 as the best number of clusters
## * 1 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_single_m## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 1.2110 48.6294 30.7199 -16.6876 68.7971 2080310 2630470.33 2418.8114
## 3 1.4687 42.6332 33.4613 -19.1743 112.2717 3905176 1921788.95 2142.2946
## 4 0.7132 43.4048 133.6979 -28.3906 156.4042 5776407 1529582.40 1877.2509
## 5 2.1139 84.0625 16.8337 -23.4437 336.8583 4255349 760872.97 1198.3600
## 6 0.6854 75.1131 2.1426 -24.9786 357.7335 5617238 659894.86 1118.2560
## 7 0.9542 63.2530 0.2792 -27.1668 360.3148 7563891 645744.90 1108.1096
## 8 1.9672 54.0886 13.5292 -29.1924 361.8786 9815204 645786.16 1106.7831
## 9 2.7313 51.5555 31.3605 -30.0696 378.2332 11604057 562615.81 1045.7967
## 10 0.0695 55.2926 141.6699 -29.6203 443.9265 10895543 400447.15 920.7906
## 11 7.0128 94.1712 5.1567 -23.2732 597.4925 6952601 149776.21 569.8117
## 12 0.7867 87.6224 0.7704 -24.3566 621.6371 7482268 149273.06 557.2630
## 13 0.9748 80.3024 0.2563 -25.6432 622.9010 8735149 148372.50 555.3863
## 14 6.7540 73.9017 13.6456 -26.8762 623.4187 10108878 147912.30 554.7600
## 15 0.1985 73.4148 3.1447 -27.1054 662.5682 9857935 128269.88 523.1715
## 16 0.8212 69.3781 0.4964 -27.9923 679.6850 10444066 127946.53 515.9602
## 17 0.9994 64.9260 0.4330 -29.0087 680.5920 11745898 127166.62 514.8193
## 18 1.0061 60.9763 0.4549 -29.9777 682.4360 13067620 127151.28 513.8215
## 19 0.9913 57.4719 0.3142 -30.8992 683.5683 14491378 126887.74 512.7707
## 20 0.9842 54.2942 0.1198 -31.7897 684.1661 16016986 126615.91 512.0428
## 21 7.5035 51.3790 8.9974 -32.6572 684.6560 17622716 126480.23 511.7641
## 22 0.1148 51.1366 23.0090 -32.8608 712.3318 17234499 114429.54 491.5685
## 23 0.4449 54.7577 43.0318 -32.0832 786.5739 13824944 88769.92 444.6386
## 24 3.7186 64.3365 0.3669 -30.0060 866.1681 10804373 68857.97 371.0568
## 25 0.9796 61.4898 0.1719 -30.7446 868.2853 11620531 68701.78 370.4275
## 26 0.9932 58.8095 0.1053 -31.4737 868.6110 12551719 68615.15 370.1316
## 27 3.4458 56.3151 10.2579 -32.1859 869.2832 13497949 68619.87 369.9496
## 28 0.3132 56.9523 0.3015 -32.1439 882.8648 13717646 61251.93 352.9518
## 29 0.9847 54.7477 0.1755 -32.8032 884.8873 14591488 61240.39 352.4505
## 30 4.2932 52.6591 8.6567 -33.4545 885.2095 15594201 61103.15 352.1576
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale Ratkowsky
## 2 0.2986 1.2043 0.1799 0.1428 0.8402 0.8857 30.5908 0.1285 0.2432
## 3 0.5365 1.3598 0.1711 0.2605 0.7153 0.9478 12.9338 0.0548 0.2567
## 4 0.7943 1.5518 0.2011 0.2277 0.7242 0.6381 132.7118 0.5647 0.2515
## 5 2.3146 2.4309 0.2464 0.3668 0.7359 0.9685 7.4493 0.0324 0.2825
## 6 2.5948 2.6050 0.2426 0.3736 0.6658 0.2093 11.3367 2.8342 0.2623
## 7 2.6280 2.6288 0.2426 0.2823 0.6692 150.1282 0.0000 0.0000 0.2438
## 8 2.6418 2.6320 0.2426 0.2524 0.6728 0.9830 3.9514 0.0173 0.2286
## 9 2.8503 2.7855 0.2409 0.2531 0.6640 0.8802 30.9075 0.1356 0.2208
## 10 3.4100 3.1636 0.2527 0.2787 0.6589 0.6172 138.9573 0.6176 0.2350
## 11 6.7234 5.1123 0.2322 0.4183 0.6561 0.4562 8.3432 1.0429 0.2356
## 12 7.0386 5.2274 0.2321 0.3865 0.6450 16.1084 -0.9379 -0.4690 0.2303
## 13 7.0765 5.2451 0.2321 0.3594 0.6454 85.4573 0.0000 0.0000 0.2214
## 14 7.0823 5.2510 0.2321 0.3280 0.6519 0.9855 3.1535 0.0146 0.2134
## 15 7.4535 5.5680 0.2699 0.3240 0.6498 0.3039 11.4530 1.9088 0.2138
## 16 7.6980 5.6459 0.2698 0.2973 0.6388 14.8400 -0.9326 -0.4663 0.2092
## 17 7.7113 5.6584 0.2698 0.2719 0.6269 13.7872 -1.8549 -0.6183 0.2031
## 18 7.7496 5.6694 0.2698 0.2656 0.6297 23.2289 -0.9570 -0.4785 0.1975
## 19 7.7808 5.6810 0.2698 0.2549 0.6325 25.6870 -0.9611 -0.4805 0.1923
## 20 7.7988 5.6890 0.2698 0.2213 0.6273 78.7103 0.0000 0.0000 0.1875
## 21 7.8042 5.6921 0.2699 0.2031 0.6241 1.0069 -1.4752 -0.0069 0.1830
## 22 8.1177 5.9260 0.2987 0.2089 0.6100 0.9044 22.5142 0.1052 0.1822
## 23 9.1169 6.5515 0.2996 0.2229 0.5555 0.8341 41.5606 0.1979 0.1850
## 24 11.9508 7.8506 0.2908 0.2249 0.5570 1.2847 -0.4432 -0.1477 0.1832
## 25 11.9912 7.8640 0.2909 0.2316 0.5494 162.4400 0.0000 0.0000 0.1796
## 26 12.0051 7.8703 0.2909 0.2206 0.5542 566.9647 0.0000 0.0000 0.1761
## 27 12.0235 7.8741 0.2909 0.2110 0.5570 0.9565 9.3135 0.0452 0.1729
## 28 12.4989 8.2534 0.3188 0.2112 0.5605 1.8280 -0.4529 -0.2265 0.1703
## 29 12.5478 8.2651 0.3188 0.2022 0.5497 26.2760 -1.9239 -0.6413 0.1674
## 30 12.5548 8.2720 0.3188 0.2050 0.5442 0.9631 7.8098 0.0381 0.1646
## Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex SDbw
## 2 1209.4057 0.4634 42.9060 0.0012 0.3730 7e-04 2.8306 2.2319 0.4329
## 3 714.0982 0.5245 -0.5211 0.0049 0.2058 7e-04 1.9036 2.1032 0.2894
## 4 469.3127 0.6105 6.0529 0.0063 0.2201 7e-04 1.5281 2.0092 0.2051
## 5 239.6720 0.7578 9.1267 0.0148 0.2710 6e-04 1.4469 1.7103 0.1559
## 6 186.3760 0.7635 195.2827 0.0169 0.2341 6e-04 1.5329 1.6607 0.1196
## 7 158.3014 0.7625 -246.1966 0.0169 0.1981 6e-04 1.5653 1.6433 0.0684
## 8 138.3479 0.7623 7.8480 0.0169 0.1933 6e-04 2.4444 1.6365 0.0813
## 9 116.1996 0.7683 6.8330 0.0190 0.1841 6e-04 2.4169 1.5935 0.0671
## 10 92.0791 0.7817 5.0232 0.0251 0.1892 6e-04 2.3277 1.4978 0.0644
## 11 51.8011 0.7999 25.0764 0.0435 0.1918 6e-04 2.3932 1.2436 0.0625
## 12 46.4386 0.7990 -226.7415 0.0437 0.1912 6e-04 2.3568 1.2246 0.0336
## 13 42.7220 0.7988 -67.4430 0.0437 0.1733 6e-04 2.3814 1.2186 0.0274
## 14 39.6257 0.7986 2.6097 0.0437 0.1644 6e-04 3.4833 1.2139 0.0240
## 15 34.8781 0.8037 67.8652 0.0454 0.1907 6e-04 3.3151 1.1867 0.0220
## 16 32.2475 0.8028 -108.1028 0.0456 0.1903 6e-04 3.3498 1.1701 0.0178
## 17 30.2835 0.8026 -74.2588 0.0457 0.1623 6e-04 3.4333 1.1654 0.0156
## 18 28.5456 0.8022 -68.6613 0.0457 0.1464 6e-04 3.5397 1.1620 0.0208
## 19 26.9879 0.8020 -42.6971 0.0458 0.1432 6e-04 3.5177 1.1580 0.0181
## 20 25.6021 0.8018 -36.6149 0.0458 0.1397 6e-04 4.4548 1.1525 0.0158
## 21 24.3697 0.8017 4.5555 0.0458 0.1233 6e-04 5.3981 1.1494 0.0143
## 22 22.3440 0.8008 6.9552 0.0480 0.1273 6e-04 5.3255 1.1275 0.0089
## 23 19.3321 0.7797 4.5730 0.0583 0.1337 6e-04 5.2722 1.0659 0.0085
## 24 15.4607 0.7684 -31.3861 0.0679 0.1359 6e-04 5.3168 0.9836 0.0080
## 25 14.8171 0.7682 -24.3112 0.0679 0.1350 6e-04 5.3379 0.9809 0.0073
## 26 14.2358 0.7681 -23.7413 0.0680 0.1304 6e-04 5.4003 0.9777 0.0065
## 27 13.7018 0.7680 4.1002 0.0680 0.1261 6e-04 6.5367 0.9752 0.0060
## 28 12.6054 0.7654 -28.8377 0.0704 0.1388 6e-04 6.6103 0.9541 0.0056
## 29 12.1535 0.7652 -23.6452 0.0704 0.1362 6e-04 6.6785 0.9506 0.0050
## 30 11.7386 0.7650 4.4478 0.0705 0.1249 6e-04 6.6747 0.9479 0.0046
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.5221 216.9679 0.8794
## 3 0.5214 215.7172 0.9467
## 4 0.5211 215.0914 0.5689
## 5 0.5193 211.9589 0.9681
## 6 -0.4219 -10.1102 0.1360
## 7 -1.0633 0.0000 NaN
## 8 0.5190 211.3316 0.9829
## 9 0.5186 210.7040 0.8733
## 10 0.5175 208.8197 0.5397
## 11 -0.1409 -56.6808 0.3783
## 12 -0.7431 -2.3458 1.0000
## 13 -1.0633 0.0000 NaN
## 14 0.5142 203.1521 0.9855
## 15 -0.2510 -24.9172 0.1985
## 16 -0.7431 -2.3458 1.0000
## 17 -0.5522 -5.6219 1.0000
## 18 -0.7431 -2.3458 1.0000
## 19 -0.7431 -2.3458 1.0000
## 20 -1.0633 0.0000 NaN
## 21 0.5138 202.5209 1.0000
## 22 0.5134 201.8895 0.9002
## 23 0.5118 199.3611 0.8205
## 24 -0.5522 -5.6219 1.0000
## 25 -1.0633 0.0000 NaN
## 26 -1.0633 0.0000 NaN
## 27 0.5102 196.8282 0.9558
## 28 -0.7431 -2.3458 1.0000
## 29 -0.5522 -5.6219 1.0000
## 30 0.5098 196.1942 0.9626
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 21.0000 11.0000 11.0000 2.0000 5.0000 11 5.0
## Value_Index 7.5035 94.1712 136.5132 -16.6876 180.4541 4472610 768709.4
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 5.0000 11.0000 11.0000 3.0000 2.0000 2.0000 2.0000
## Value_Index 598.7869 3.3133 -1.8335 0.1711 0.1428 0.8402 0.8857
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 2.0000 2.0000 5.0000 3.0000 15.0000 2.000 2.0000
## Value_Index 30.5908 0.1285 0.2825 495.3075 0.8037 42.906 0.0012
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 2.000 0 5.0000 0 30.0000
## Value_Index 0.373 0 1.4469 0 0.0046
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 1 1 1 1 1 1 1 1 1 1
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 1 1 1 1 1 1 1 1 1 1 1
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 1 1 1 1 1 1 1 1 1 1 1
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 1 1 1 1 1 1 1 1 1 1 1
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 1 1 1 1 1 1 1 1 1 1 1
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 1 1 1 1 1 1 1 1 1 1 1
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 1 1 1 1 1 1 1 1 1 1 1
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 1 1 1 1 1 1 1 1 1 1 1
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 1 1 1 1 1 1 1 1 1 1 1
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 1 1 1 1 1 1 1 1 1 1 1
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 1 1 1 1 1 1 1 1 1 1 1
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 1 1 1 2 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 1 1 1 1 1 1 1 1 1 1 1
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 1 1 1 1 1 1 1 1 1 1 1
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 1 1 1 1 1 1 1 1 1 1 1
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 1 1 1 1 1 1 1 1 1 1 1
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 1 1 1 1 1 1 1 1 1 1 1
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 1 1 1 1 1 1 1 1 1 1 1
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 1 1 1 1 1 1 1 1 1 1 1
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 1 1 1 1 1 1 1 1 1 1 1
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 1 1 1 1 1 1 1 1 1 1 1
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 1 1 1 1 1 1 1 1 1testH.nbclust_complete_m <- NbClust(data_aseg_pca$x[,1:2], distance="manhattan", min.nc=2, max.nc=30, method="complete", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 6 proposed 2 as the best number of clusters
## * 8 proposed 3 as the best number of clusters
## * 1 proposed 5 as the best number of clusters
## * 1 proposed 6 as the best number of clusters
## * 1 proposed 8 as the best number of clusters
## * 2 proposed 9 as the best number of clusters
## * 3 proposed 18 as the best number of clusters
## * 1 proposed 26 as the best number of clusters
## * 1 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 3
##
##
## *******************************************************************testH.nbclust_complete_m## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW
## 2 1.0429 48.6294 339.1812 -16.6876 68.7971 2080310.0 2630470.3313
## 3 3.1869 227.5966 27.7615 -8.4444 358.0676 1402355.7 501929.3637
## 4 0.9737 178.0040 117.9434 -14.6297 453.7646 1673270.4 476450.8236
## 5 2.0664 228.7350 22.1363 -10.9916 627.1591 1269458.1 163880.2810
## 6 0.7412 203.7813 9.9775 -12.4803 677.4846 1482223.8 127640.7561
## 7 0.2968 177.9578 181.9329 -14.3350 689.5667 1918421.9 115771.0401
## 8 46.7755 296.3520 25.9219 -6.8475 898.4002 1049617.7 40620.4474
## 9 0.0540 290.2648 97.4192 -7.1327 945.1801 1093163.6 34264.5569
## 10 21.7103 376.0141 19.7836 -3.1617 1069.6227 803551.7 12992.1960
## 11 0.2755 367.8934 9.7999 -3.5057 1102.9188 846345.7 10323.9131
## 12 9.7117 348.1251 17.8833 -4.3765 1125.8418 915470.5 10031.4481
## 13 0.1152 344.1190 8.2288 -4.5836 1172.9567 882899.6 9619.1495
## 14 1.2072 328.3433 8.7969 -5.3415 1197.0427 926180.6 9417.8115
## 15 0.7788 315.9818 6.0013 -5.9730 1222.8750 954722.3 9068.0616
## 16 0.5289 301.8351 32.1583 -6.7223 1235.7640 1029463.6 8502.6126
## 17 0.2130 324.1510 144.9046 -5.6792 1354.1678 709594.3 7917.7694
## 18 21.4356 509.5539 6.3866 1.2728 1522.2114 394977.5 2028.2005
## 19 3.9160 493.2131 10.1337 0.7071 1540.6600 407521.5 2027.5124
## 20 0.3447 486.9997 6.7641 0.4499 1560.2985 416069.9 1865.0929
## 21 1.0381 475.0434 6.4462 0.0017 1573.2168 434678.7 1705.0803
## 22 0.2193 463.9181 29.4971 -0.4298 1586.5012 451373.8 1624.3021
## 23 4.4917 501.7780 13.8520 0.7245 1671.7599 345832.5 1406.7350
## 24 1.2592 508.8460 5.5674 0.8756 1701.8645 332167.1 1294.9003
## 25 0.4213 498.1282 17.0022 0.4771 1722.6175 330567.6 1295.4788
## 26 2.4119 514.2962 4.8215 0.9047 1753.3028 314630.0 1107.7929
## 27 2.3840 503.4789 6.4766 0.5047 1767.6183 319651.0 1089.9952
## 28 0.5185 497.4669 4.8968 0.2476 1779.6299 326985.9 1005.5009
## 29 0.5049 488.6395 12.6724 -0.1017 1788.0275 338698.2 942.5363
## 30 0.0622 498.1895 149.9712 0.1265 1824.3425 311562.6 896.5542
## TraceW Friedman Rubin Cindex DB Silhouette Duda Pseudot2
## 2 2418.8114 0.2986 1.2043 0.1799 0.1428 0.8402 0.4123 337.7560
## 3 997.3941 3.0192 2.9206 0.1874 0.4695 0.7355 0.5118 13.3558
## 4 892.8128 4.3767 3.2628 0.2187 0.6847 0.6847 0.6201 135.3768
## 5 595.3037 6.2569 4.8934 0.1999 0.7630 0.6428 0.6434 4.4336
## 6 544.0553 6.8928 5.3543 0.2948 0.6876 0.6405 0.3034 9.1842
## 7 521.8060 7.1978 5.5826 0.3003 0.6137 0.6390 0.4842 222.5968
## 8 293.0132 16.0955 9.9417 0.2712 0.6612 0.5686 0.3000 23.3370
## 9 263.5645 19.3898 11.0525 0.2921 0.6092 0.5722 0.5900 129.9550
## 10 185.3831 28.1535 15.7136 0.2295 0.7140 0.4870 0.1863 8.7348
## 11 170.7002 31.5790 17.0652 0.2519 0.6962 0.4900 12.4791 -0.9199
## 12 163.6950 34.3513 17.7955 0.2883 0.6092 0.4951 0.5067 19.4684
## 13 151.7893 36.7001 19.1913 0.3062 0.6430 0.4906 0.3673 6.8894
## 14 146.4794 37.9868 19.8870 0.3131 0.6310 0.4890 0.2746 10.5660
## 15 140.9914 39.1253 20.6611 0.3241 0.6296 0.4904 4.9738 -3.1958
## 16 137.3285 39.3862 21.2122 0.3355 0.6035 0.4915 0.3006 55.8339
## 17 120.0882 47.8714 24.2575 0.3569 0.5679 0.4625 0.4616 187.7929
## 18 72.7897 72.7681 40.0199 0.2537 0.6293 0.4591 41.7462 0.0000
## 19 70.7542 76.1858 41.1712 0.2616 0.5798 0.4669 0.5612 8.5992
## 20 67.6521 82.0677 43.0591 0.2731 0.5749 0.4632 0.2698 5.4126
## 21 65.6341 82.8726 44.3830 0.2967 0.5635 0.4648 16.1084 -0.9379
## 22 63.7574 87.1728 45.6894 0.3044 0.5343 0.4651 0.5027 38.5849
## 23 56.1587 94.4369 51.8715 0.2972 0.5584 0.4307 0.3470 13.1726
## 24 52.7890 105.5190 55.1827 0.3003 0.5575 0.4325 105.5903 0.0000
## 25 51.4625 111.2365 56.6050 0.3309 0.5320 0.4365 0.3636 26.2499
## 26 47.6911 124.1455 61.0813 0.3414 0.5418 0.4338 23.2289 -0.9570
## 27 46.6403 130.6979 62.4575 0.3518 0.5276 0.4365 0.5938 6.1559
## 28 45.2640 131.5491 64.3566 0.3510 0.5585 0.4332 0.2650 8.3195
## 29 44.2420 132.5159 65.8432 0.3779 0.5606 0.4346 0.4334 26.1470
## 30 41.7355 151.3932 69.7976 0.3875 0.5644 0.4273 0.3119 264.6791
## Beale Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex
## 2 1.4191 0.2432 1209.4057 0.4634 12.1881 0.0012 0.3730 7e-04 2.7265
## 3 0.8904 0.3267 332.4647 0.7609 6.4633 0.0317 0.0859 6e-04 2.8044
## 4 0.6098 0.3194 223.2032 0.7609 3.8653 0.0323 0.1007 6e-04 2.4468
## 5 0.4926 0.3704 119.0607 0.7844 2.9835 0.0567 0.0888 6e-04 2.3370
## 6 1.8368 0.3489 90.6759 0.7846 8.4291 0.0569 0.1312 6e-04 2.0682
## 7 1.0600 0.3240 74.5437 0.7843 4.7533 0.0570 0.1337 6e-04 1.7940
## 8 2.1215 0.3114 36.6266 0.7005 2.3491 0.1131 0.1096 6e-04 1.7820
## 9 0.6912 0.2946 29.2849 0.7002 3.8561 0.1135 0.1185 6e-04 1.6952
## 10 2.9116 0.2861 18.5383 0.6011 0.3800 0.1911 0.0516 6e-04 2.3432
## 11 -0.4599 0.2738 15.5182 0.6012 0.7213 0.1910 0.0567 6e-04 2.1785
## 12 0.9271 0.2625 13.6412 0.6012 3.3828 0.1910 0.0649 6e-04 1.9684
## 13 1.3779 0.2556 11.6761 0.5984 2.4950 0.1935 0.0695 6e-04 2.4060
## 14 2.1132 0.2478 10.4628 0.5983 2.3584 0.1936 0.0711 6e-04 2.4450
## 15 -0.6392 0.2409 9.3994 0.5981 2.0042 0.1938 0.0737 6e-04 2.4791
## 16 2.2334 0.2341 8.5830 0.5980 3.2133 0.1939 0.0763 6e-04 2.4541
## 17 1.1592 0.2313 7.0640 0.5944 2.8819 0.1971 0.0821 6e-04 2.4453
## 18 0.0000 0.2277 4.0439 0.4672 0.4705 0.3280 0.0507 6e-04 3.0565
## 19 0.7166 0.2219 3.7239 0.4672 1.1765 0.3279 0.0524 6e-04 3.0807
## 20 1.8042 0.2163 3.3826 0.4668 1.0891 0.3280 0.0549 6e-04 3.1691
## 21 -0.4690 0.2115 3.1254 0.4667 1.0061 0.3279 0.0597 6e-04 3.2486
## 22 0.9646 0.2066 2.8981 0.4667 3.0524 0.3279 0.0612 6e-04 3.1897
## 23 1.6466 0.2037 2.4417 0.4542 1.4347 0.3444 0.0621 6e-04 4.3341
## 24 0.0000 0.1995 2.1995 0.4538 0.6873 0.3446 0.0629 6e-04 4.4119
## 25 1.6406 0.1956 2.0585 0.4538 2.0176 0.3446 0.0694 6e-04 4.3169
## 26 -0.4785 0.1919 1.8343 0.4524 1.5285 0.3460 0.0721 6e-04 5.3605
## 27 0.6156 0.1883 1.7274 0.4524 3.4549 0.3460 0.0743 6e-04 5.4041
## 28 2.0799 0.1851 1.6166 0.4515 2.3633 0.3473 0.0743 6e-04 5.5066
## 29 1.2451 0.1820 1.5256 0.4513 6.1030 0.3475 0.0800 6e-04 5.5671
## 30 2.1874 0.1790 1.3912 0.4473 1.6010 0.3543 0.0825 6e-04 6.4458
## Dindex SDbw
## 2 2.2319 0.4329
## 3 1.5958 0.7475
## 4 1.5212 0.3123
## 5 1.2984 0.2867
## 6 1.2570 0.2298
## 7 1.2358 0.1695
## 8 0.9574 0.1449
## 9 0.9134 0.1163
## 10 0.7724 0.1531
## 11 0.7527 0.1317
## 12 0.7370 0.0994
## 13 0.7106 0.0633
## 14 0.6986 0.0442
## 15 0.6839 0.0379
## 16 0.6739 0.0331
## 17 0.6280 0.0369
## 18 0.4879 0.0355
## 19 0.4795 0.0289
## 20 0.4722 0.0275
## 21 0.4666 0.0202
## 22 0.4606 0.0171
## 23 0.4314 0.0232
## 24 0.4207 0.0247
## 25 0.4139 0.0216
## 26 0.3987 0.0169
## 27 0.3947 0.0151
## 28 0.3889 0.0146
## 29 0.3842 0.0137
## 30 0.3737 0.0119
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.5221 216.9679 0.2429
## 3 0.0647 202.2234 0.4218
## 4 0.5164 206.9329 0.5439
## 5 -0.0987 -89.0644 0.6200
## 6 -0.3258 -16.2785 0.2206
## 7 0.5118 199.3611 0.3474
## 8 -0.0307 -335.8023 0.1460
## 9 0.5022 185.3717 0.5016
## 10 -0.5522 -5.6219 0.1658
## 11 -0.7431 -2.3458 1.0000
## 12 0.1556 108.5678 0.4040
## 13 -0.3258 -16.2785 0.3061
## 14 -0.3258 -16.2785 0.1833
## 15 -0.3258 -16.2785 1.0000
## 16 0.1977 97.3833 0.1182
## 17 0.4884 168.6482 0.3150
## 18 -1.0633 0.0000 NaN
## 19 -0.0027 -4016.9908 0.4995
## 20 -0.5522 -5.6219 0.2764
## 21 -0.7431 -2.3458 1.0000
## 22 0.2963 92.6281 0.3856
## 23 -0.1409 -56.6808 0.2279
## 24 -1.0633 0.0000 NaN
## 25 0.0832 165.3574 0.2108
## 26 -0.7431 -2.3458 1.0000
## 27 -0.0624 -153.2995 0.5513
## 28 -0.4219 -10.1102 0.2060
## 29 0.1556 108.5678 0.2988
## 30 0.4583 141.8551 0.1144
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 8.0000 26.0000 3.0000 18.0000 3.0000 3.0 3
## Value_Index 46.7755 514.2962 311.4197 1.2728 289.2705 948869.1 2128541
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 3.000 18.0000 18.0000 2.0000 2.0000 2.0000 3.0000
## Value_Index 1316.836 24.8967 -14.6111 0.1799 0.1428 0.8402 0.5118
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 3.0000 2.0000 5.0000 3.000 6.0000 9.0000 2.0000
## Value_Index 13.3558 1.4191 0.3704 876.941 0.7846 3.8561 0.0012
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 2.000 0 9.0000 0 30.0000
## Value_Index 0.373 0 1.6952 0 0.0119
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 1 2 2 2 2 2 2 2 2 2
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 2 2 2 2 2 2 2 2 2 2 2
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 2 2 2 2 2 2 2 2 2 2 2
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 2 2 2 2 2 2 2 2 2 2 2
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 2 2 2 2 2 2 2 2 2 2 2
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 2 2 2 2 2 2 2 2 2 2 2
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 2 2 2 2 2 2 2 2 2 2 2
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 2 2 2 2 2 2 2 2 2 2 2
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 2 2 2 2 2 2 2 2 2 2 2
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 2 2 2 2 2 2 2 2 2 2 2
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 2 2 2 2 2 2 2 2 2 2 2
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 2 2 2 3 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 1 1 1 1 1 1 1 2 2 2 2
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 2 2 2 2 2 2 2 2 2 2 2
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 2 2 2 2 2 2 2 2 2 2 2
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 2 2 2 2 2 2 2 2 2 2 2
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 2 2 2 2 2 2 2 2 2 2 2
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 2 2 2 2 2 2 2 2 2 2 2
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 2 2 2 2 2 2 2 2 2 2 2
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 2 2 2 2 2 2 2 2 2 2 2
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 2 2 2 2 2 2 2 2 2 2 2
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 2 2 2 2 2 2 2 2 2testH.nbclust_Average_m <- NbClust(data_aseg_pca$x[,1:2], distance="manhattan", min.nc=2, max.nc=30, method="average", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 5 proposed 2 as the best number of clusters
## * 3 proposed 3 as the best number of clusters
## * 3 proposed 4 as the best number of clusters
## * 2 proposed 5 as the best number of clusters
## * 1 proposed 7 as the best number of clusters
## * 1 proposed 9 as the best number of clusters
## * 2 proposed 19 as the best number of clusters
## * 4 proposed 20 as the best number of clusters
## * 2 proposed 29 as the best number of clusters
## * 1 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_Average_m## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 0.1968 274.4417 19.0073 -6.6822 239.8246 1020102.0 849235.5138 1352.9393
## 3 0.9469 157.0207 211.7353 -11.6452 283.8989 1910165.5 786561.2153 1252.8812
## 4 2.2941 267.6462 13.3443 -9.0833 485.3988 1466635.5 144564.9250 661.7104
## 5 1.7325 214.5081 23.8748 -11.8950 532.8083 1880839.8 140147.2487 626.2974
## 6 0.6434 192.9911 8.1381 -13.2438 627.3663 1826442.1 141724.4623 568.5369
## 7 1.0245 167.0585 6.8216 -15.2139 640.2403 2356152.0 133986.5879 549.4288
## 8 0.2270 147.7230 232.1784 -16.9322 657.0259 2869542.4 130892.0093 533.8006
## 9 9.8157 286.3972 6.8068 -7.3356 895.9090 1342283.2 26472.7982 266.7977
## 10 1.2906 261.6953 9.3717 -8.6922 907.0658 1581868.1 24161.6499 259.1611
## 11 1.1310 244.9899 33.3116 -9.6981 923.1039 1790332.5 21727.6912 249.0147
## 12 0.9830 257.0170 7.0423 -9.0036 1016.5733 1443352.3 21077.8516 217.3917
## 13 0.9720 242.3949 5.8635 -9.9215 1041.2497 1528421.4 20916.9583 210.8782
## 14 0.8810 228.9666 3.7693 -10.8219 1063.0482 1618701.6 20693.8588 205.5683
## 15 0.5141 215.4695 41.4896 -11.7837 1069.2011 1811170.0 19967.0830 202.1960
## 16 2.0347 239.8833 1.7541 -10.2194 1177.5591 1312007.4 17035.6513 170.7162
## 17 2.1784 225.7489 18.8297 -11.1923 1185.8329 1430942.5 17036.5948 169.3898
## 18 0.5643 230.4795 2.6997 -10.9371 1285.4184 1059408.5 16746.0797 156.2005
## 19 0.0800 219.4791 257.5850 -11.7374 1294.1870 1138041.9 16485.1397 154.3238
## 20 52.1676 461.7343 6.4114 -0.3784 1542.3298 448416.7 2286.7795 71.2633
## 21 0.9702 449.6981 5.8256 -0.8500 1553.0799 472723.7 2104.4898 69.2454
## 22 1.4642 437.9451 13.0753 -1.3240 1563.6670 496428.0 1962.1127 67.4511
## 23 1.2276 441.6707 12.0265 -1.2571 1594.4692 477230.4 1778.5352 63.6344
## 24 0.4868 444.3473 3.8314 -1.2293 1616.0238 474996.7 1544.0502 60.2929
## 25 0.7920 431.5387 2.2974 -1.7498 1627.3460 491654.4 1527.9590 59.2420
## 26 1.1049 416.8481 2.7027 -2.3544 1631.2794 523129.0 1479.7228 58.6157
## 27 0.9576 404.0843 2.2963 -2.9048 1636.4714 552070.3 1433.8924 57.8847
## 28 0.0921 391.5512 90.8560 -3.4621 1643.7528 575979.2 1431.5687 57.2673
## 29 28.8059 540.0650 4.4390 1.4523 1793.2992 331339.7 460.4302 40.0872
## 30 0.9169 530.0413 3.9670 1.0888 1805.0215 337681.9 448.8534 39.2613
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale
## 2 1.5632 2.1531 0.1576 0.4914 0.7866 1.3159 -1.6803 -0.2100
## 3 1.9460 2.3251 0.2466 0.3740 0.7676 0.5008 228.2815 0.9925
## 4 5.0874 4.4023 0.1944 0.6207 0.6861 0.4844 6.3872 0.9125
## 5 5.3994 4.6512 0.2044 0.5589 0.6838 0.4343 18.2324 1.2155
## 6 6.4446 5.1237 0.2991 0.6272 0.6644 3.2042 -2.7516 -0.5503
## 7 6.7795 5.3019 0.2990 0.5493 0.6667 0.4482 8.6177 1.0772
## 8 7.1666 5.4572 0.2988 0.5406 0.6252 0.4561 253.9865 1.1869
## 9 18.3181 10.9185 0.2409 0.5962 0.5788 3.1934 -3.4343 -0.5724
## 10 18.9063 11.2402 0.2407 0.5449 0.5778 0.2093 11.3367 2.8342
## 11 20.0795 11.6983 0.2406 0.4892 0.5813 0.4774 30.6508 1.0569
## 12 23.4624 13.3999 0.2938 0.5228 0.5539 0.4556 5.9757 0.9960
## 13 24.5174 13.8138 0.3284 0.5627 0.5565 0.3673 6.8894 1.3779
## 14 25.4271 14.1706 0.3283 0.5697 0.5572 10.4573 -1.8087 -0.6029
## 15 26.0090 14.4070 0.3283 0.4978 0.5628 0.8074 43.6672 0.2373
## 16 39.4014 17.0636 0.3044 0.5167 0.4280 150.1282 0.0000 0.0000
## 17 40.4081 17.1972 0.3044 0.4874 0.4320 0.4126 25.6227 1.3486
## 18 52.8533 18.6493 0.3031 0.5123 0.4394 16.1084 -0.9379 -0.4690
## 19 54.7352 18.8761 0.3031 0.4805 0.4398 0.3632 305.0321 1.7430
## 20 90.0544 40.8771 0.2071 0.5028 0.5209 0.2698 5.4126 1.8042
## 21 90.7475 42.0683 0.2069 0.4907 0.5216 2.0677 -5.1638 -0.4694
## 22 93.7773 43.1874 0.2064 0.4775 0.5173 0.4067 11.6687 1.2965
## 23 105.7526 45.7777 0.2055 0.4832 0.5192 0.1815 27.0508 3.8644
## 24 106.5701 48.3148 0.2050 0.4802 0.5072 23.2289 -0.9570 -0.4785
## 25 111.1454 49.1718 0.2049 0.4702 0.5085 85.4573 0.0000 0.0000
## 26 111.9794 49.6972 0.2049 0.4377 0.5152 52.0690 0.0000 0.0000
## 27 112.1719 50.3248 0.2048 0.4130 0.5207 71.2689 0.0000 0.0000
## 28 114.0355 50.8674 0.2048 0.3798 0.5260 0.4980 69.5640 0.9938
## 29 131.1427 72.6674 0.2678 0.4059 0.5095 3.8916 -1.4861 -0.4954
## 30 132.0288 74.1962 0.2677 0.3953 0.5112 25.6870 -0.9611 -0.4805
## Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex
## 2 0.3478 676.4696 0.7583 2.8041 0.0146 0.1731 6e-04 3.4366 1.8034
## 3 0.3132 417.6271 0.7593 5.8314 0.0146 0.2710 6e-04 1.4350 1.7616
## 4 0.3482 165.4276 0.8070 3.9233 0.0461 0.0823 6e-04 1.5008 1.3562
## 5 0.3388 125.2595 0.8070 7.2888 0.0462 0.0866 6e-04 1.3975 1.3244
## 6 0.3364 94.7561 0.8055 7.2553 0.0469 0.1273 6e-04 1.4093 1.2775
## 7 0.3123 78.4898 0.8053 12.7777 0.0470 0.1273 6e-04 1.1689 1.2580
## 8 0.2937 66.7251 0.8047 4.8852 0.0471 0.1273 6e-04 1.2207 1.2381
## 9 0.2876 29.6442 0.6928 2.0771 0.1203 0.0909 6e-04 1.2186 0.9129
## 10 0.2737 25.9161 0.6928 3.0799 0.1203 0.0909 6e-04 1.2886 0.9002
## 11 0.2615 22.6377 0.6927 4.4030 0.1204 0.0909 6e-04 1.2606 0.8829
## 12 0.2596 18.1160 0.6878 4.8527 0.1237 0.1125 6e-04 1.6044 0.8364
## 13 0.2512 16.2214 0.6875 6.8980 0.1239 0.1258 6e-04 1.8144 0.8209
## 14 0.2435 14.6835 0.6872 7.5328 0.1241 0.1258 6e-04 1.8614 0.8089
## 15 0.2354 13.4797 0.6871 6.0459 0.1241 0.1258 6e-04 1.9258 0.8011
## 16 0.2291 10.6698 0.6396 5.8046 0.1573 0.1212 6e-04 1.9663 0.7352
## 17 0.2225 9.9641 0.6396 6.0591 0.1573 0.1212 6e-04 2.1986 0.7284
## 18 0.2191 8.6778 0.6367 8.0527 0.1596 0.1212 6e-04 2.3624 0.7009
## 19 0.2133 8.1223 0.6366 2.9206 0.1596 0.1212 6e-04 2.3509 0.6948
## 20 0.2150 3.5632 0.4551 0.9904 0.3459 0.0426 6e-04 2.5285 0.4630
## 21 0.2101 3.2974 0.4550 1.1313 0.3458 0.0426 6e-04 2.5997 0.4574
## 22 0.2054 3.0660 0.4548 1.2866 0.3458 0.0426 6e-04 2.6537 0.4517
## 23 0.2009 2.7667 0.4543 1.3633 0.3460 0.0426 6e-04 2.9843 0.4396
## 24 0.1973 2.5122 0.4540 1.5775 0.3462 0.0426 6e-04 2.9995 0.4261
## 25 0.1934 2.3697 0.4539 1.5834 0.3462 0.0426 6e-04 3.0387 0.4222
## 26 0.1897 2.2544 0.4539 1.6770 0.3462 0.0426 6e-04 3.3926 0.4175
## 27 0.1863 2.1439 0.4539 1.6847 0.3462 0.0426 6e-04 3.3972 0.4124
## 28 0.1830 2.0453 0.4538 1.4984 0.3463 0.0426 6e-04 3.4967 0.4078
## 29 0.1821 1.3823 0.4242 1.8024 0.3615 0.0691 6e-04 3.8374 0.3504
## 30 0.1792 1.3087 0.4241 1.9087 0.3615 0.0691 6e-04 3.9050 0.3469
## SDbw
## 2 0.8774
## 3 0.6590
## 4 0.3541
## 5 0.2266
## 6 0.1755
## 7 0.1121
## 8 0.0887
## 9 0.0857
## 10 0.0730
## 11 0.0512
## 12 0.0734
## 13 0.0666
## 14 0.0587
## 15 0.0441
## 16 0.0342
## 17 0.0293
## 18 0.0305
## 19 0.0298
## 20 0.0231
## 21 0.0209
## 22 0.0149
## 23 0.0132
## 24 0.0117
## 25 0.0102
## 26 0.0091
## 27 0.0076
## 28 0.0066
## 29 0.0063
## 30 0.0056
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 -0.1409 -56.6808 1.0000
## 3 0.5193 211.9589 0.3714
## 4 -0.1908 -37.4469 0.4277
## 5 0.0647 202.2234 0.3117
## 6 -0.3258 -16.2785 1.0000
## 7 -0.1409 -56.6808 0.3672
## 8 0.5134 201.8895 0.3062
## 9 -0.2510 -24.9172 1.0000
## 10 -0.4219 -10.1102 0.1360
## 11 0.2311 93.1391 0.3544
## 12 -0.2510 -24.9172 0.4032
## 13 -0.3258 -16.2785 0.3061
## 14 -0.5522 -5.6219 1.0000
## 15 0.5003 182.8126 0.7889
## 16 -1.0633 0.0000 NaN
## 17 0.1299 120.5893 0.2724
## 18 -0.7431 -2.3458 1.0000
## 19 0.4957 177.0365 0.1765
## 20 -0.5522 -5.6219 0.2764
## 21 -0.0307 -335.8023 1.0000
## 22 -0.0987 -89.0644 0.3007
## 23 -0.1908 -37.4469 0.0506
## 24 -0.7431 -2.3458 1.0000
## 25 -1.0633 0.0000 NaN
## 26 -1.0633 0.0000 NaN
## 27 -1.0633 0.0000 NaN
## 28 0.3888 108.4601 0.3728
## 29 -0.5522 -5.6219 1.0000
## 30 -0.7431 -2.3458 1.0000
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 20.0000 29.000 19.0000 29.0000 20.0000 9 4.0
## Value_Index 52.1676 540.065 254.8853 1.4523 248.1427 1766844 641996.3
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 4.0000 20.0000 20.0000 2.0000 3.000 2.0000 2.0000
## Value_Index 555.7577 35.3193 -20.8097 0.1576 0.374 0.7866 1.3159
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 5.0000 2.00 4.0000 3.0000 5.000 19.0000 2.0000
## Value_Index 18.2324 -0.21 0.3482 258.8426 0.807 2.9206 0.0146
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 3.000 0 7.0000 0 30.0000
## Value_Index 0.271 0 1.1689 0 0.0056
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 2 2 2 2 2 2 2 2 2 2
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 2 2 2 2 2 2 2 2 2 2 2
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 2 2 2 2 2 2 2 2 2 2 2
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 2 2 2 2 2 2 2 2 2 2 2
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 2 2 2 2 2 2 2 2 2 2 2
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 2 2 2 2 2 2 2 2 2 2 2
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 2 2 2 2 2 2 2 2 2 2 2
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 2 2 2 2 2 2 2 2 2 2 2
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 2 2 2 2 2 2 2 2 2 2 2
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 2 2 2 2 2 2 2 2 2 2 2
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 2 2 2 2 2 2 2 2 2 2 2
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 2 2 2 1 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 2 2 2 2 2 2 2 2 2 2 2
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 2 2 2 2 2 2 2 2 2 2 2
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 2 2 2 2 2 2 2 2 2 2 2
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 2 2 2 2 2 2 2 2 2 2 2
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 2 2 2 2 2 2 2 2 2 2 2
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 2 2 2 2 2 2 2 2 2 2 2
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 2 2 2 2 2 2 2 2 2 2 2
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 2 2 2 2 2 2 2 2 2 2 2
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 2 2 2 2 2 2 2 2 2 2 2
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 2 2 2 2 2 2 2 2 2#testH.nbclust<-NbClust(data_aseg_pca$x[,1:2], distance="manhattan", min.nc=2, max.nc=30, method="ward.D", index="all")
testH.nbclust_ward_m <- NbClust(data_aseg_pca$x[,1:2], distance="euclidean", min.nc=2, max.nc=30, method="ward.D2", index="all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
##
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 5 proposed 2 as the best number of clusters
## * 5 proposed 3 as the best number of clusters
## * 5 proposed 4 as the best number of clusters
## * 1 proposed 6 as the best number of clusters
## * 1 proposed 9 as the best number of clusters
## * 1 proposed 11 as the best number of clusters
## * 1 proposed 12 as the best number of clusters
## * 1 proposed 27 as the best number of clusters
## * 1 proposed 29 as the best number of clusters
## * 3 proposed 30 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 2
##
##
## *******************************************************************testH.nbclust_ward_m## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW TraceW
## 2 5.1126 394.2464 97.4622 -3.0642 281.8735 856157.21 325460.6253 1096.5701
## 3 0.3975 325.2050 135.5389 -4.9574 411.8507 1120816.12 206645.2458 777.9825
## 4 66.1171 384.3429 59.8005 -3.7062 593.7157 933934.17 45772.8915 494.9332
## 5 0.0308 374.6551 74.2538 -3.6856 690.8346 973629.52 36645.6607 394.8751
## 6 3.2412 407.5380 47.3904 -2.1576 849.2645 724548.86 21913.9141 300.0631
## 7 1.5894 414.5143 38.5365 -1.7654 919.7744 735138.78 15445.8636 249.5279
## 8 0.3357 417.7662 45.2860 -1.5731 985.3506 730616.20 11905.9794 214.1149
## 9 1.4389 440.6524 37.3019 -0.7072 1074.2321 638495.47 9077.9256 179.1459
## 10 0.5906 457.0987 44.0324 -0.1256 1144.6973 587708.28 5053.4029 154.2393
## 11 0.8607 492.4003 47.5260 1.0298 1247.7802 462820.26 3721.6416 129.4556
## 12 1.9453 542.4792 33.3643 2.5266 1327.1991 395618.19 2066.6447 107.2063
## 13 1.1097 570.3088 30.9811 3.2791 1384.3966 365845.90 1808.5203 93.5210
## 14 1.8100 598.0246 23.7744 3.9835 1448.3096 325097.10 1701.8688 82.2900
## 15 0.9355 612.7001 23.3674 4.3171 1507.6806 291409.72 1567.4002 74.4573
## 16 0.8209 629.9888 24.5564 4.7022 1551.0297 276769.79 1421.9014 67.4521
## 17 0.8780 653.9637 25.6803 5.2328 1597.5660 257375.02 1232.1655 60.7881
## 18 0.8115 684.8006 28.7757 5.8969 1647.6910 234158.20 842.6328 54.5107
## 19 1.3488 728.8892 24.3975 6.8141 1704.5326 205879.59 523.6842 48.2558
## 20 1.4254 764.5668 20.2494 7.4995 1750.4778 188375.94 465.3844 43.4582
## 21 0.9830 790.5950 20.1705 7.9582 1796.8272 171211.11 341.2341 39.7953
## 22 1.2739 819.4976 17.7679 8.4530 1843.8563 154467.37 327.9413 36.4392
## 23 1.3602 842.9272 15.3244 8.8253 1878.8799 145904.84 313.8831 33.6931
## 24 1.0118 859.9023 14.9367 9.0668 1909.0507 140100.83 244.7565 31.4706
## 25 0.9004 877.5994 15.3502 9.3140 1942.1836 132416.55 244.5250 29.4351
## 26 0.9296 899.0594 15.6898 9.6194 1973.1230 125898.95 221.7340 27.4736
## 27 1.2121 924.1260 14.1798 9.9760 2005.9531 118411.81 194.8258 25.5969
## 28 1.3228 945.2078 12.4028 10.2543 2035.8910 112411.08 156.3931 23.9993
## 29 0.9453 960.6637 12.4780 10.4327 2065.5055 106585.90 156.3964 22.6728
## 30 0.9179 978.1617 12.7843 10.6389 2097.7616 99718.77 156.3033 21.4069
## Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale
## 2 2.2068 2.6565 0.0911 0.6943 0.7611 0.4248 28.4357 1.2925
## 3 4.0161 3.7443 0.1311 0.7588 0.6882 0.4784 234.3723 1.0851
## 4 8.7187 5.8857 0.0768 0.8854 0.4925 1.3159 -1.6803 -0.2100
## 5 12.8001 7.3771 0.1310 0.7391 0.4970 0.5753 61.2619 0.7293
## 6 25.3827 9.7081 0.0975 0.8880 0.4739 0.3661 45.0129 1.6671
## 7 25.9801 11.6742 0.0934 0.7500 0.4910 0.4844 6.3872 0.9125
## 8 26.6738 13.6050 0.1062 0.7118 0.4933 0.4745 13.2905 1.0223
## 9 27.8481 16.2607 0.1044 0.7138 0.4964 0.3155 282.0429 2.1530
## 10 33.9375 18.8865 0.0854 0.7445 0.4512 0.4914 56.9232 1.0165
## 11 36.0356 22.5022 0.0651 0.7232 0.4922 0.3034 9.1842 1.8368
## 12 48.6111 27.1722 0.0793 0.6961 0.4952 0.4861 7.4012 0.9251
## 13 58.8411 31.1485 0.1246 0.6839 0.4972 0.5347 17.4050 0.8288
## 14 61.8379 35.3996 0.1165 0.7300 0.4905 0.2819 12.7343 2.1224
## 15 64.2855 39.1236 0.1152 0.7057 0.4927 12.4791 -0.9199 -0.4599
## 16 74.0391 43.1868 0.1559 0.6380 0.4968 0.3638 40.2140 1.6756
## 17 87.7910 47.9212 0.1473 0.6366 0.4897 0.4275 84.3585 1.3181
## 18 93.8148 53.4397 0.1158 0.6354 0.4970 0.5357 26.0043 0.8388
## 19 108.1605 60.3665 0.0990 0.6687 0.5018 0.4708 12.3641 1.0303
## 20 126.8929 67.0308 0.0941 0.6792 0.5035 4.9738 -3.1958 -0.6392
## 21 133.2075 73.2005 0.1024 0.6559 0.5071 0.3212 6.3387 1.5847
## 22 137.7178 79.9424 0.1113 0.6537 0.5078 0.4162 30.8602 1.3417
## 23 152.0875 86.4581 0.1026 0.6514 0.5118 0.4212 9.6202 1.2025
## 24 166.0320 92.5637 0.1004 0.6433 0.5104 41.7462 0.0000 0.0000
## 25 177.4482 98.9646 0.1002 0.6096 0.5167 0.2192 21.3710 3.0530
## 26 198.6676 106.0303 0.0985 0.5889 0.5239 16.1084 -0.9379 -0.4690
## 27 225.0476 113.8041 0.1175 0.5642 0.5250 0.3715 10.1499 1.4500
## 28 231.6725 121.3802 0.1157 0.5626 0.5279 105.5903 0.0000 0.0000
## 29 245.8728 128.4814 0.1155 0.5403 0.5317 0.5470 27.3313 0.8039
## 30 262.3889 136.0795 0.1022 0.5602 0.5313 0.4722 15.6515 1.0434
## Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex
## 2 0.3214 548.2851 0.7951 1.1143 0.0390 0.0805 7e-04 9.7204 1.5709
## 3 0.3577 259.3275 0.8026 6.6768 0.0396 0.1182 7e-04 6.3281 1.4121
## 4 0.3481 123.7333 0.4935 -0.4630 0.2852 0.0126 7e-04 5.5625 1.0167
## 5 0.3252 78.9750 0.4946 0.6809 0.2836 0.0215 7e-04 3.2461 0.9750
## 6 0.3007 50.0105 0.4943 0.2784 0.2766 0.0215 7e-04 3.7235 0.8311
## 7 0.3096 35.6468 0.4960 -0.0909 0.2706 0.0215 7e-04 3.4418 0.7732
## 8 0.3063 26.7644 0.4966 0.1971 0.2691 0.0247 7e-04 3.0994 0.7414
## 9 0.3027 19.9051 0.4975 5.5429 0.2665 0.0247 7e-04 2.9770 0.7054
## 10 0.2904 15.4239 0.3603 0.5826 0.5459 0.0126 7e-04 4.6099 0.5648
## 11 0.2850 11.7687 0.3482 -0.0075 0.5049 0.0126 7e-04 4.6876 0.5036
## 12 0.2735 8.9339 0.3486 0.0539 0.4994 0.0155 7e-04 4.2723 0.4824
## 13 0.2636 7.1939 0.3489 0.3743 0.4929 0.0248 7e-04 4.3061 0.4681
## 14 0.2567 5.8779 0.3478 0.1814 0.4748 0.0248 7e-04 4.4313 0.4426
## 15 0.2500 4.9638 0.3478 0.0434 0.4711 0.0248 7e-04 4.4740 0.4242
## 16 0.2424 4.2158 0.3479 0.7300 0.4701 0.0336 7e-04 4.0885 0.4085
## 17 0.2354 3.5758 0.3447 1.6306 0.4616 0.0336 7e-04 4.3746 0.3839
## 18 0.2297 3.0284 0.3092 0.4479 0.4943 0.0336 8e-04 5.8798 0.3485
## 19 0.2241 2.5398 0.3051 0.2860 0.4495 0.0336 8e-04 6.0191 0.3309
## 20 0.2186 2.1729 0.3046 0.1253 0.4332 0.0336 8e-04 6.1843 0.3183
## 21 0.2140 1.8950 0.3046 0.1788 0.4295 0.0369 8e-04 6.2006 0.3083
## 22 0.2097 1.6563 0.3046 0.7275 0.4258 0.0405 8e-04 6.2532 0.2984
## 23 0.2053 1.4649 0.3010 0.4489 0.4087 0.0405 8e-04 6.3744 0.2849
## 24 0.2011 1.3113 0.3005 0.1295 0.4029 0.0405 8e-04 6.5510 0.2766
## 25 0.1972 1.1774 0.3005 0.4602 0.4021 0.0405 8e-04 6.5045 0.2682
## 26 0.1934 1.0567 0.3001 0.1818 0.3975 0.0405 8e-04 6.6241 0.2581
## 27 0.1899 0.9480 0.3001 0.4860 0.3962 0.0485 8e-04 6.4344 0.2520
## 28 0.1867 0.8571 0.2997 0.2017 0.3920 0.0485 8e-04 6.5617 0.2448
## 29 0.1836 0.7818 0.2997 1.5887 0.3914 0.0485 8e-04 6.3656 0.2381
## 30 0.1806 0.7136 0.2876 0.8137 0.3864 0.0485 8e-04 9.9723 0.2280
## SDbw
## 2 1.0724
## 3 0.7017
## 4 0.5998
## 5 0.2718
## 6 0.2466
## 7 0.1942
## 8 0.1640
## 9 0.1296
## 10 0.1237
## 11 0.1293
## 12 0.1005
## 13 0.0847
## 14 0.0876
## 15 0.0742
## 16 0.0531
## 17 0.0606
## 18 0.0662
## 19 0.0560
## 20 0.0513
## 21 0.0448
## 22 0.0367
## 23 0.0356
## 24 0.0284
## 25 0.0253
## 26 0.0203
## 27 0.0204
## 28 0.0191
## 29 0.0142
## 30 0.0136
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.1671 104.6547 0.2853
## 3 0.5142 203.1521 0.3388
## 4 -0.1409 -56.6808 1.0000
## 5 0.4140 117.4720 0.4838
## 6 0.2153 94.7474 0.1987
## 7 -0.1908 -37.4469 0.4277
## 8 0.0222 529.7343 0.3749
## 9 0.4669 148.4332 0.1182
## 10 0.3548 100.0055 0.3652
## 11 -0.3258 -16.2785 0.2206
## 12 -0.1409 -56.6808 0.4194
## 13 0.1556 108.5678 0.4439
## 14 -0.2510 -24.9172 0.1705
## 15 -0.7431 -2.3458 1.0000
## 16 0.1881 99.2518 0.1984
## 17 0.3756 104.7312 0.2713
## 18 0.2454 92.2265 0.4372
## 19 -0.0027 -4016.9908 0.3735
## 20 -0.3258 -16.2785 1.0000
## 21 -0.4219 -10.1102 0.2802
## 22 0.1780 101.6241 0.2719
## 23 -0.1409 -56.6808 0.3296
## 24 -1.0633 0.0000 NaN
## 25 -0.1908 -37.4469 0.0848
## 26 -0.7431 -2.3458 1.0000
## 27 -0.1908 -37.4469 0.2729
## 28 -1.0633 0.0000 NaN
## 29 0.2646 91.7349 0.4519
## 30 0.0647 202.2234 0.3655
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 4.0000 30.0000 4.0000 30.0000 4.0000 6.0 4.0
## Value_Index 66.1171 978.1617 75.7384 10.6389 181.8649 259670.6 160872.4
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 4.0000 27.00 12.0000 11.0000 29.0000 2.0000 2.0000
## Value_Index 182.9912 26.38 -0.6938 0.0651 0.5403 0.7611 0.4248
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 2.0000 2.0000 3.0000 3.0000 3.0000 3.0000 2.000
## Value_Index 28.4357 1.2925 0.3577 288.9576 0.8026 6.6768 0.039
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 3.0000 0 9.000 0 30.0000
## Value_Index 0.1182 0 2.977 0 0.0136
##
## $Best.partition
## e_1 e_2 e_3 e_4 e_5 e_6 e_7 e_8 e_9 e_10 e_11
## 1 1 1 1 2 2 2 2 2 2 2
## e_12 e_13 e_14 e_15 e_16 e_17 e_18 e_19 e_20 e_21 e_22
## 2 2 2 2 2 2 2 2 2 2 2
## e_23 e_24 e_25 e_26 e_27 e_28 e_29 e_30 e_31 e_32 e_33
## 2 2 2 2 2 2 2 2 2 2 2
## e_34 e_35 e_36 e_37 e_38 e_39 e_40 e_41 e_42 e_43 e_44
## 2 2 2 2 2 2 2 2 2 2 2
## e_45 e_46 e_47 e_48 e_49 e_50 e_51 e_52 e_53 e_54 e_55
## 2 2 2 2 2 2 2 2 2 2 2
## e_56 e_57 e_58 e_59 e_60 e_61 e_62 e_63 e_64 e_65 e_66
## 2 2 2 2 2 2 2 2 2 2 2
## e_67 e_68 e_69 e_70 e_71 e_72 e_73 e_74 e_75 e_76 e_77
## 2 2 2 2 2 2 2 2 2 2 2
## e_78 e_79 e_80 e_81 e_82 e_83 e_84 e_85 e_86 e_87 e_88
## 2 2 2 2 2 2 2 2 2 2 2
## e_89 e_90 e_91 e_92 e_93 e_94 e_95 e_96 e_97 e_98 e_99
## 2 2 2 2 2 2 2 2 2 2 2
## e_100 e_101 e_102 e_103 e_104 e_105 e_106 e_107 e_108 e_109 e_110
## 2 2 2 2 2 2 2 2 2 2 2
## e_111 e_112 e_113 e_114 e_115 e_116 e_117 e_118 e_119 e_120 e_121
## 2 2 2 2 2 2 2 2 2 2 2
## e_122 e_123 e_124 ip_1 ip_2 ip_3 ip_4 ip_5 ip_6 ip_7 ip_8
## 2 2 2 1 1 1 1 1 1 1 1
## ip_9 ip_10 ip_11 ip_12 ip_13 ip_14 ip_15 ip_16 ip_17 ip_18 ip_19
## 1 1 1 1 1 1 1 1 1 1 1
## ip_20 ip_21 ip_22 ip_23 ip_24 ip_25 ip_26 ip_27 ip_28 ip_29 ip_30
## 2 2 2 2 2 2 2 2 2 2 2
## ip_31 ip_32 ip_33 ip_34 ip_35 ip_36 ip_37 ip_38 ip_39 ip_40 ip_41
## 2 2 2 2 2 2 2 2 2 2 2
## ip_42 ip_43 ip_44 ip_45 ip_46 ip_47 ip_48 ip_49 ip_50 ip_51 ip_52
## 2 2 2 2 2 2 2 2 2 2 2
## ip_53 ip_54 ip_55 ip_56 ip_57 ip_58 ip_59 ip_60 ip_61 ip_62 ip_63
## 2 2 2 2 2 2 2 2 2 2 2
## ip_64 ip_65 ip_66 ip_67 ip_68 ip_69 ip_70 ip_71 ip_72 ip_73 ip_74
## 2 2 2 2 2 2 2 2 2 2 2
## ip_75 ip_76 ip_77 ip_78 ip_79 ip_80 ip_81 ip_82 ip_83 ip_84 ip_85
## 2 2 2 2 2 2 2 2 2 2 2
## ip_86 ip_87 ip_88 ip_89 ip_90 ip_91 ip_92 ip_93 ip_94 ip_95 ip_96
## 2 2 2 2 2 2 2 2 2 2 2
## ip_97 ip_98 ip_99 ip_100 ip_101 ip_102 ip_103 ip_104 ip_105 ip_106 ip_107
## 2 2 2 2 2 2 2 2 2 2 2
## ip_108 ip_109 ip_110 ip_111 ip_112 ip_113 ip_114 ip_115 ip_116
## 2 2 2 2 2 2 2 2 2# EVALUACION - Clustering Jerarquico
# Ancho de la Silueta
hclust_clusters <- eclust(x = data_aseg_pca$x[,1:2], FUNcluster = "hclust", k = 4, seed = 123,
hc_metric = "manhattan", nstart = 30, graph = FALSE, method="ward.D2")
fviz_silhouette(sil.obj = hclust_clusters, print.summary = TRUE, palette = "jco",
ggtheme = theme_classic()) ## cluster size ave.sil.width
## 1 1 9 0.40
## 2 2 20 0.12
## 3 3 35 0.40
## 4 4 176 0.63
#Evaluacion Indice Dunn
hc_indiceD <- cluster.stats(d = dist(data_aseg_pca$x[,1:2], method = "manhattan"),clustering=hclust_clusters$cluster)
hc_indiceD$average.within## [1] 1.914112hc_indiceD$average.between## [1] 7.125497hc_indiceD$dunn## [1] 0.02816942# Indice de Davies Bouldin
print(index.DB(data_aseg_pca$x[,1:2], hclust_clusters$cluster, centrotypes="centroids"))## $DB
## [1] 0.9581487
##
## $r
## [1] 0.7934449 1.1629173 1.1629173 0.7133152
##
## $R
## [,1] [,2] [,3] [,4]
## [1,] Inf 0.7934449 0.4903633 0.3614094
## [2,] 0.7934449 Inf 1.1629173 0.5891873
## [3,] 0.4903633 1.1629173 Inf 0.7133152
## [4,] 0.3614094 0.5891873 0.7133152 Inf
##
## $d
## 1 2 3 4
## 1 0.000000 8.932438 11.396632 14.362820
## 2 8.932438 0.000000 3.453352 6.141223
## 3 11.396632 3.453352 0.000000 2.971229
## 4 14.362820 6.141223 2.971229 0.000000
##
## $S
## [1] 4.3299627 2.7574352 1.2585274 0.8608956
##
## $centers
## [,1] [,2]
## [1,] -12.864465 -1.1615525
## [2,] -4.407428 1.7136853
## [3,] -1.511288 -0.1672741
## [4,] 1.459226 -0.1020747# Conectividad Modelo Clustering Jerarquico
d = dist(data_aseg_pca$x[,1:2], method = "manhattan")
connectivity(d,hclust_clusters$cluster,neighbSize = 10)## [1] 23.86429# Estabilidad modelo Clustering Jerárquico con clValid()
estabilidad_h<-clValid(data_aseg_norm, 4, clMethods = "hierarchical",
validation = "stability", maxitems=600,
metric = "manhattan", method='ward')
summary(estabilidad_h)##
## Clustering Methods:
## hierarchical
##
## Cluster sizes:
## 4
##
## Validation Measures:
## 4
##
## hierarchical APN 0.1116
## AD 4.9158
## ADM 0.3843
## FOM 0.5342
##
## Optimal Scores:
##
## Score Method Clusters
## APN 0.1116 hierarchical 4
## AD 4.9158 hierarchical 4
## ADM 0.3843 hierarchical 4
## FOM 0.5342 hierarchical 4# Evaluacion exahustiva con clusterboot()
testH.clusterboot<-clusterboot(data_aseg_pca$x[,1:2],B=70,bootmethod=c("jitter","boot"),clustermethod=hclustCBI, method="ward.D", k=4, seed=123)## jitter 1
## jitter 2
## jitter 3
## jitter 4
## jitter 5
## jitter 6
## jitter 7
## jitter 8
## jitter 9
## jitter 10
## jitter 11
## jitter 12
## jitter 13
## jitter 14
## jitter 15
## jitter 16
## jitter 17
## jitter 18
## jitter 19
## jitter 20
## jitter 21
## jitter 22
## jitter 23
## jitter 24
## jitter 25
## jitter 26
## jitter 27
## jitter 28
## jitter 29
## jitter 30
## jitter 31
## jitter 32
## jitter 33
## jitter 34
## jitter 35
## jitter 36
## jitter 37
## jitter 38
## jitter 39
## jitter 40
## jitter 41
## jitter 42
## jitter 43
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## jitter 45
## jitter 46
## jitter 47
## jitter 48
## jitter 49
## jitter 50
## jitter 51
## jitter 52
## jitter 53
## jitter 54
## jitter 55
## jitter 56
## jitter 57
## jitter 58
## jitter 59
## jitter 60
## jitter 61
## jitter 62
## jitter 63
## jitter 64
## jitter 65
## jitter 66
## jitter 67
## jitter 68
## jitter 69
## jitter 70
## boot 1
## boot 2
## boot 3
## boot 4
## boot 5
## boot 6
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## boot 11
## boot 12
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## boot 50
## boot 51
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## boot 53
## boot 54
## boot 55
## boot 56
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## boot 60
## boot 61
## boot 62
## boot 63
## boot 64
## boot 65
## boot 66
## boot 67
## boot 68
## boot 69
## boot 70testH.clusterboot## * Cluster stability assessment *
## Cluster method: hclust/cutree
## Full clustering results are given as parameter result
## of the clusterboot object, which also provides further statistics
## of the resampling results.
## Number of resampling runs: 70
##
## Number of clusters found in data: 4
##
## Clusterwise Jaccard jittering mean:
## [1] 1 1 1 1
## dissolved:
## [1] 0 0 0 0
## recovered:
## [1] 70 70 70 70
## Clusterwise Jaccard bootstrap (omitting multiple points) mean:
## [1] 0.8204666 0.7250066 0.7617709 0.6511095
## dissolved:
## [1] 7 6 0 31
## recovered:
## [1] 53 34 42 363.3.2.- Ejecución del modelo Clustering Jerárquico
# EJECUCION DEL CLUSTERING JERARQUICO UTILIZANDO LA METRICA MANHATTAN
hc_euclidea_single <- hclust(d = dist(x=data_aseg_pca$x[,1:2], method="manhattan"),method="ward.D2")
fviz_dend(x = hc_euclidea_single, k = 4, cex = 0.6, show_labels=FALSE) +
geom_hline(yintercept = 20, linetype = "dashed") +
labs(title = "Clustering Jerárquico", subtitle = "Distancia Manhattan, Linkage Ward")
# Grafico Arbol Filogenetico
Phylo = fviz_dend(hclust_clusters, cex = 0.8, lwd = 0.8, k = 4,
rect = TRUE,
k_colors = "jco",
rect_border = "jco",
rect_fill = TRUE,
type = "phylogenic")
Phylo
# Clusters modelo Clustering Jerárquico en las dos primeras componentes principales
fviz_cluster(hclust_clusters,data_aseg_pca$x[,1:2])
# Clusters - modelo Clustering Jerárquico - en las tres primeras componentes principales
plot3d(data_aseg_pca$x[,1:3],type="s", col=hclust_clusters$cluster, size=1)
rglwidget()# Asignación de clusters al dataset
#datos_cluster_h <- data.frame(data_aseg, cluster = as.factor(hclust_clusters$cluster))
#datos_cluster_h
#write.csv(datos_cluster_h, "mi_HC_nK_20230610-1651.csv")3.4.- Modelo basado en K-medoids
3.4.1.- Determinación del número óptimo de clusters y evaluación del modelo K-medoids
# MODELO BASADO EN K-MEDOIDS
# Determinacion del numero optimo de clusters
## Metodo del Codo con diferentes distancias
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "euclidean")) + labs(subtitle = "Metodo del Codo_ Dist-Euclidean_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "manhattan")) + labs(subtitle = "Metodo del Codo_Dist-Manhattan_K-medoids") 
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "pearson")) + labs(subtitle = "Metodo del Codo_Dist-Pearson_K-medoids") 
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "wss", k.max=30, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "spearman")) + labs(subtitle = "Metodo del Codo_Dist-Spearman_K-medoids") 
## Metodo de la Silueta con diferentes distancias
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "silhouette", k.max=10, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "euclidean")) + labs(subtitle = "Metodo de la Silueta-Euclidean_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "silhouette", k.max=10, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "manhattan")) + labs(subtitle = "Metodo de la Silueta-Manhattan_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "silhouette", k.max=10, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "pearson")) + labs(subtitle = "Metodo de la Silueta-Pearson_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method = "silhouette", k.max=10, nstart=30, diss = get_dist(data_aseg_pca$x[,1:2], method = "spearman")) + labs(subtitle = "Metodo de la Silueta-Spearman_K-medoids")
## Metodo Gap Statistic con diferentes distancias
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method ="gap_stat", nstart=1, k.max=10, diss = get_dist(data_aseg_pca$x[,1:2], method = "euclidean")) + labs(subtitle = "Metodo Gap Stat-Euclidean_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method ="gap_stat", nstart=1, k.max=10, diss = get_dist(data_aseg_pca$x[,1:2], method = "manhattan")) + labs(subtitle = "Metodo Gap Stat-Manhattan_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method ="gap_stat", nstart=1, k.max=10, diss = get_dist(data_aseg_pca$x[,1:2], method = "Pearson")) + labs(subtitle = "Metodo Gap Stat-Pearson_K-medoids")
fviz_nbclust(data_aseg_pca$x[,1:2], pam, method ="gap_stat", nstart=1, k.max=10, diss = get_dist(data_aseg_pca$x[,1:2], method = "Spearman")) + labs(subtitle = "Metodo Gap Stat-Spearman_K-medoids")
# Clustering con PAM
pam_clusters <- eclust(x = data_aseg_pca$x[,1:2], FUNcluster = "pam", k = 4, seed = 123,
hc_metric = "manhattan", nstart=30, graph = FALSE)
fviz_cluster(pam_clusters,data_aseg_pca$x[,1:2])
#EVALUACION modelo K-medoids
# Ancho de la Silueta
fviz_silhouette(sil.obj = pam_clusters, print.summary = TRUE, palette = "jco",
ggtheme = theme_classic()) ## cluster size ave.sil.width
## 1 1 10 0.42
## 2 2 44 0.17
## 3 3 95 0.27
## 4 4 91 0.81
head(pam_clusters$silinfo$widths)| cluster | neighbor | sil_width | |
|---|---|---|---|
| ip_3 | 1 | 2 | 0.6095839 |
| ip_5 | 1 | 2 | 0.6075852 |
| ip_2 | 1 | 2 | 0.5654247 |
| ip_4 | 1 | 2 | 0.5352343 |
| ip_6 | 1 | 2 | 0.4500389 |
| ip_1 | 1 | 2 | 0.4291083 |
# Indice Dunn
pam_indiceD <- cluster.stats(d = dist(data_aseg_pca$x[,1:2], method = "manhattan"), clustering=pam_clusters$cluster)
pam_indiceD$average.within## [1] 1.668909pam_indiceD$average.between## [1] 5.23319pam_indiceD$dunn## [1] 0.005867191# indice Davies-Bouldin DB
d<-dist(data_aseg_pca$x[,1:2], method = "manhattan")
print(index.DB(data_aseg_pca$x[,1:2], pam_clusters$cluster,d, centrotypes="medoids"))## $DB
## [1] 0.9759078
##
## $r
## [1] 0.7724723 1.1488748 1.1488748 0.8334091
##
## $R
## [,1] [,2] [,3] [,4]
## [1,] Inf 0.7724723 0.4532964 0.3753697
## [2,] 0.7724723 Inf 1.1488748 0.6728783
## [3,] 0.4532964 1.1488748 Inf 0.8334091
## [4,] 0.3753697 0.6728783 0.8334091 Inf
##
## $d
## 1 2 3 4
## 1 0.000000 9.472437 12.309124 13.358501
## 2 9.472437 0.000000 3.006989 4.294014
## 3 12.309124 3.006989 0.000000 1.382077
## 4 13.358501 4.294014 1.382077 0.000000
##
## $S
## [1] 4.7211115 2.5960835 0.8585702 0.2932657
##
## $centers
## [,1] [,2]
## [1,] -11.1129384 -2.2030014
## [2,] -2.0329367 0.4952620
## [3,] 0.9594637 0.1994216
## [4,] 2.1391919 -0.5205640# Conectividad Modelo K-medoids
connectivity(d,pam_clusters$cluster,neighbSize = 10)## [1] 28.36984# Medidas de estabilidad - K-medoids
estabilidad_pam<-clValid(data_aseg_norm, 4, clMethods = "pam",
validation = "stability", maxitems = 600,
metric = "manhattan")
summary(estabilidad_pam)##
## Clustering Methods:
## pam
##
## Cluster sizes:
## 4
##
## Validation Measures:
## 4
##
## pam APN 0.0436
## AD 4.6022
## ADM 0.1715
## FOM 0.5015
##
## Optimal Scores:
##
## Score Method Clusters
## APN 0.0436 pam 4
## AD 4.6022 pam 4
## ADM 0.1715 pam 4
## FOM 0.5015 pam 4