PFM Master BigData
Joaquin Moreno
12/5/2020
1. Introducción
Realizacion del Proyecto Fin de Master BigData 2019/2020 Vamos a realizar un analisis del dataset seleccionado “Breast Cancer Wisconsin” para presentar un modelo de Machine Learning que sea capaz de realizar predicciones sobre la diagnosis de un paciente dado, determinando si el cáncer que padece es Maligno o Benigno(M = malignant, B = benign). El dataset se encuentra disponible en la direccion https://www.kaggle.com/uciml/breast-cancer-wisconsin-data y la descripcion de las variables y de el tipo de cancer( variable objetivo) se encuentra tambien disponible en https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29 descargando el fichero wdbc.names podemos encontrar el numero de observaciones y la descripcion de las variables.
Es interesante indicar, que las caracteristicas han sido obtenidas mediante un proceso computacional analizando imagenes de los nucleos de las celulas tumorales de las pacientes.
2. Carga de datos
Descargamos el archivo y leemos el contenido del fichero con las caracteristicas.
# descarga de ficheros
#fileURL <- "https://www.kaggle.com/uciml/breast-cancer-wisconsin-data/download/breast-cancer-wisconsin-data.zip"
fileURL <- "https://query.data.world/s/d3ikssglnxd5hn3257bokisfg2qvtp"
if(! "downloader" %in% installed.packages())
install.packages("downloader")
library(downloader)## Warning: package 'downloader' was built under R version 3.6.3download(fileURL,"F:/colmenar/master big data/PFM/datos/breast-cancer-wisconsin-data.zip", mode ="wb")
unzip("F:/colmenar/master big data/PFM/datos/breast-cancer-wisconsin-data.zip", exdir="F:/colmenar/master big data/PFM/datos")
fechaDescarga <- date()
fechaDescarga## [1] "Thu Aug 06 18:07:47 2020"con <- file("F:/colmenar/master big data/PFM/datos/data.csv","r")
breastCan <- read.csv(con)
close(con)
kable(head(breastCan[,1:5]))| id | diagnosis | radius_mean | texture_mean | perimeter_mean |
|---|---|---|---|---|
| 842302 | M | 17.99 | 10.38 | 122.80 |
| 842517 | M | 20.57 | 17.77 | 132.90 |
| 84300903 | M | 19.69 | 21.25 | 130.00 |
| 84348301 | M | 11.42 | 20.38 | 77.58 |
| 84358402 | M | 20.29 | 14.34 | 135.10 |
| 843786 | M | 12.45 | 15.70 | 82.57 |
3. Analisis descriptivo
Vamos a ir realizando una serie de estudios para ir conociendo el dataset y sus características Observaciones y variables del dataset
dim(breastCan) # observaciones y variables del dataset## [1] 569 33str(breastCan)## 'data.frame': 569 obs. of 33 variables:
## $ id : int 842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
## $ diagnosis : Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ...
## $ radius_mean : num 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave.points_mean : num 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave.points_se : num 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num 0.712 0.242 0.45 0.687 0.4 ...
## $ concave.points_worst : num 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num 0.1189 0.089 0.0876 0.173 0.0768 ...
## $ X : logi NA NA NA NA NA NA ...Vemos que hay: - Un campo de tipo factor con la variable objetivo - Todas las variables predictoras son numéricas - Hay una columna con valores NA
Busqueda de observaciones con valores nulos:
any(is.na.data.frame(breastCan)) # buscamos valores nulos## [1] TRUEPaso de todos los nombres de las columnas a minusculas
names(breastCan) <- tolower(names(breastCan)) # nombres de las variables a minusculas
names(breastCan)## [1] "id" "diagnosis"
## [3] "radius_mean" "texture_mean"
## [5] "perimeter_mean" "area_mean"
## [7] "smoothness_mean" "compactness_mean"
## [9] "concavity_mean" "concave.points_mean"
## [11] "symmetry_mean" "fractal_dimension_mean"
## [13] "radius_se" "texture_se"
## [15] "perimeter_se" "area_se"
## [17] "smoothness_se" "compactness_se"
## [19] "concavity_se" "concave.points_se"
## [21] "symmetry_se" "fractal_dimension_se"
## [23] "radius_worst" "texture_worst"
## [25] "perimeter_worst" "area_worst"
## [27] "smoothness_worst" "compactness_worst"
## [29] "concavity_worst" "concave.points_worst"
## [31] "symmetry_worst" "fractal_dimension_worst"
## [33] "x"kable(head(breastCan[,1:8])) # estructura del dataset| id | diagnosis | radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean |
|---|---|---|---|---|---|---|---|
| 842302 | M | 17.99 | 10.38 | 122.80 | 1001.0 | 0.11840 | 0.27760 |
| 842517 | M | 20.57 | 17.77 | 132.90 | 1326.0 | 0.08474 | 0.07864 |
| 84300903 | M | 19.69 | 21.25 | 130.00 | 1203.0 | 0.10960 | 0.15990 |
| 84348301 | M | 11.42 | 20.38 | 77.58 | 386.1 | 0.14250 | 0.28390 |
| 84358402 | M | 20.29 | 14.34 | 135.10 | 1297.0 | 0.10030 | 0.13280 |
| 843786 | M | 12.45 | 15.70 | 82.57 | 477.1 | 0.12780 | 0.17000 |
3.1. Añadimos nuevas variables
De la variable objetivo diagnosis la vamos a transformar en numerica creando una nueva columna “diag”, siendo 1 Maligno y 0 Benigno
breastCan$diag <- ifelse(breastCan$diagnosis =="M", 1, 0)
prop.table( table(breastCan$diag)) #proporcion respecto a la variable objetivo##
## 0 1
## 0.6274165 0.3725835Vamos a eliminar la columna X que contiene valores nulos y la columna id que no aporta nada
library(dplyr)
breastCan2 <- select(breastCan, -x,-id)
brc <- breastCan2
brc <- as.data.frame(brc)
any(is.na.data.frame(brc))## [1] FALSE str(brc)## 'data.frame': 569 obs. of 32 variables:
## $ diagnosis : Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ...
## $ radius_mean : num 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave.points_mean : num 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave.points_se : num 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num 0.712 0.242 0.45 0.687 0.4 ...
## $ concave.points_worst : num 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num 0.1189 0.089 0.0876 0.173 0.0768 ...
## $ diag : num 1 1 1 1 1 1 1 1 1 1 ...Visualizamos las variables que han quedado y sus principales valores estadísticos:
summary(brc)## diagnosis radius_mean texture_mean perimeter_mean
## B:357 Min. : 6.981 Min. : 9.71 Min. : 43.79
## M:212 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17
## Median :13.370 Median :18.84 Median : 86.24
## Mean :14.127 Mean :19.29 Mean : 91.97
## 3rd Qu.:15.780 3rd Qu.:21.80 3rd Qu.:104.10
## Max. :28.110 Max. :39.28 Max. :188.50
## area_mean smoothness_mean compactness_mean concavity_mean
## Min. : 143.5 Min. :0.05263 Min. :0.01938 Min. :0.00000
## 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492 1st Qu.:0.02956
## Median : 551.1 Median :0.09587 Median :0.09263 Median :0.06154
## Mean : 654.9 Mean :0.09636 Mean :0.10434 Mean :0.08880
## 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040 3rd Qu.:0.13070
## Max. :2501.0 Max. :0.16340 Max. :0.34540 Max. :0.42680
## concave.points_mean symmetry_mean fractal_dimension_mean
## Min. :0.00000 Min. :0.1060 Min. :0.04996
## 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770
## Median :0.03350 Median :0.1792 Median :0.06154
## Mean :0.04892 Mean :0.1812 Mean :0.06280
## 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612
## Max. :0.20120 Max. :0.3040 Max. :0.09744
## radius_se texture_se perimeter_se area_se
## Min. :0.1115 Min. :0.3602 Min. : 0.757 Min. : 6.802
## 1st Qu.:0.2324 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850
## Median :0.3242 Median :1.1080 Median : 2.287 Median : 24.530
## Mean :0.4052 Mean :1.2169 Mean : 2.866 Mean : 40.337
## 3rd Qu.:0.4789 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190
## Max. :2.8730 Max. :4.8850 Max. :21.980 Max. :542.200
## smoothness_se compactness_se concavity_se
## Min. :0.001713 Min. :0.002252 Min. :0.00000
## 1st Qu.:0.005169 1st Qu.:0.013080 1st Qu.:0.01509
## Median :0.006380 Median :0.020450 Median :0.02589
## Mean :0.007041 Mean :0.025478 Mean :0.03189
## 3rd Qu.:0.008146 3rd Qu.:0.032450 3rd Qu.:0.04205
## Max. :0.031130 Max. :0.135400 Max. :0.39600
## concave.points_se symmetry_se fractal_dimension_se
## Min. :0.000000 Min. :0.007882 Min. :0.0008948
## 1st Qu.:0.007638 1st Qu.:0.015160 1st Qu.:0.0022480
## Median :0.010930 Median :0.018730 Median :0.0031870
## Mean :0.011796 Mean :0.020542 Mean :0.0037949
## 3rd Qu.:0.014710 3rd Qu.:0.023480 3rd Qu.:0.0045580
## Max. :0.052790 Max. :0.078950 Max. :0.0298400
## radius_worst texture_worst perimeter_worst area_worst
## Min. : 7.93 Min. :12.02 Min. : 50.41 Min. : 185.2
## 1st Qu.:13.01 1st Qu.:21.08 1st Qu.: 84.11 1st Qu.: 515.3
## Median :14.97 Median :25.41 Median : 97.66 Median : 686.5
## Mean :16.27 Mean :25.68 Mean :107.26 Mean : 880.6
## 3rd Qu.:18.79 3rd Qu.:29.72 3rd Qu.:125.40 3rd Qu.:1084.0
## Max. :36.04 Max. :49.54 Max. :251.20 Max. :4254.0
## smoothness_worst compactness_worst concavity_worst concave.points_worst
## Min. :0.07117 Min. :0.02729 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.11660 1st Qu.:0.14720 1st Qu.:0.1145 1st Qu.:0.06493
## Median :0.13130 Median :0.21190 Median :0.2267 Median :0.09993
## Mean :0.13237 Mean :0.25427 Mean :0.2722 Mean :0.11461
## 3rd Qu.:0.14600 3rd Qu.:0.33910 3rd Qu.:0.3829 3rd Qu.:0.16140
## Max. :0.22260 Max. :1.05800 Max. :1.2520 Max. :0.29100
## symmetry_worst fractal_dimension_worst diag
## Min. :0.1565 Min. :0.05504 Min. :0.0000
## 1st Qu.:0.2504 1st Qu.:0.07146 1st Qu.:0.0000
## Median :0.2822 Median :0.08004 Median :0.0000
## Mean :0.2901 Mean :0.08395 Mean :0.3726
## 3rd Qu.:0.3179 3rd Qu.:0.09208 3rd Qu.:1.0000
## Max. :0.6638 Max. :0.20750 Max. :1.0000 prop.table( table(brc$diag))##
## 0 1
## 0.6274165 0.3725835Número de observaciones y variables:
dim(brc)## [1] 569 323.2.Normalizar los datos
En el summary vemos que hay mucha distancia entre los valores de unas variables y otras.Vamos a normalizar los valores para que puedan ser bien representados en las graficas:
brc_n <- as.data.frame(lapply(brc[,2:31], scale, center = TRUE, scale = TRUE))
brc_n$diag <- brc$diagVisualizamos antes
summary(brc[,c("radius_mean", "area_mean", "smoothness_mean")])## radius_mean area_mean smoothness_mean
## Min. : 6.981 Min. : 143.5 Min. :0.05263
## 1st Qu.:11.700 1st Qu.: 420.3 1st Qu.:0.08637
## Median :13.370 Median : 551.1 Median :0.09587
## Mean :14.127 Mean : 654.9 Mean :0.09636
## 3rd Qu.:15.780 3rd Qu.: 782.7 3rd Qu.:0.10530
## Max. :28.110 Max. :2501.0 Max. :0.16340Y despues de normalizar:
summary(brc_n[,c("radius_mean", "area_mean", "smoothness_mean")])## radius_mean area_mean smoothness_mean
## Min. :-2.0279 Min. :-1.4532 Min. :-3.10935
## 1st Qu.:-0.6888 1st Qu.:-0.6666 1st Qu.:-0.71034
## Median :-0.2149 Median :-0.2949 Median :-0.03486
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.4690 3rd Qu.: 0.3632 3rd Qu.: 0.63564
## Max. : 3.9678 Max. : 5.2459 Max. : 4.766723.3. Matriz de correlacion
Vamos a estudiar el grado de correlacion entra las variables.Las mas correladas entre predictoras no las voy a eliminar ya que usare los metodos de caret para que lo haga automaticamente, usando Findcorrelation:
Exportacion fichero JSON para d3 ( matriz de correlacion):
expD3Cor <- correlacion %>% select (-diag)
expD3Cor$VariableOrigen <- rownames(expD3Cor)
expD3Cor <- expD3Cor %>% filter(VariableOrigen != "diag")Gráfica con la matriz de correlación:
col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
par(mfrow=c(1,1))
corrplot(matCor, method = "shade",shade.col = NA, tl.col = "black",
tl.cex = 0.6, number.cex = 0.3, mar=c(0,0,0,0),type = "upper",addCoef.col="black",is.corr=FALSE,
diag = FALSE,order="AOE")
3.4.Reducción de la dimensionalidad: findcorrelation
# ensure the results are repeatable
set.seed(7)
# load the library
library(mlbench)
library(caret)
# calculate correlation matrix without Target
correlationMatrix <- cor(brc[,c("radius_mean","texture_mean","perimeter_mean","area_mean","smoothness_mean",
"compactness_mean","concavity_mean","concave.points_mean","symmetry_mean","fractal_dimension_mean",
"radius_se","texture_se","perimeter_se","area_se","smoothness_se","compactness_se","concavity_se",
"concave.points_se","symmetry_se","fractal_dimension_se","radius_worst","texture_worst",
"perimeter_worst","area_worst","smoothness_worst","compactness_worst","concavity_worst",
"concave.points_worst","symmetry_worst","fractal_dimension_worst")])
# summarize the correlation matrix
kable(correlationMatrix[,1:8])| radius_mean | texture_mean | perimeter_mean | area_mean | smoothness_mean | compactness_mean | concavity_mean | concave.points_mean | |
|---|---|---|---|---|---|---|---|---|
| radius_mean | 1.0000000 | 0.3237819 | 0.9978553 | 0.9873572 | 0.1705812 | 0.5061236 | 0.6767636 | 0.8225285 |
| texture_mean | 0.3237819 | 1.0000000 | 0.3295331 | 0.3210857 | -0.0233885 | 0.2367022 | 0.3024178 | 0.2934641 |
| perimeter_mean | 0.9978553 | 0.3295331 | 1.0000000 | 0.9865068 | 0.2072782 | 0.5569362 | 0.7161357 | 0.8509770 |
| area_mean | 0.9873572 | 0.3210857 | 0.9865068 | 1.0000000 | 0.1770284 | 0.4985017 | 0.6859828 | 0.8232689 |
| smoothness_mean | 0.1705812 | -0.0233885 | 0.2072782 | 0.1770284 | 1.0000000 | 0.6591232 | 0.5219838 | 0.5536952 |
| compactness_mean | 0.5061236 | 0.2367022 | 0.5569362 | 0.4985017 | 0.6591232 | 1.0000000 | 0.8831207 | 0.8311350 |
| concavity_mean | 0.6767636 | 0.3024178 | 0.7161357 | 0.6859828 | 0.5219838 | 0.8831207 | 1.0000000 | 0.9213910 |
| concave.points_mean | 0.8225285 | 0.2934641 | 0.8509770 | 0.8232689 | 0.5536952 | 0.8311350 | 0.9213910 | 1.0000000 |
| symmetry_mean | 0.1477412 | 0.0714010 | 0.1830272 | 0.1512931 | 0.5577748 | 0.6026410 | 0.5006666 | 0.4624974 |
| fractal_dimension_mean | -0.3116308 | -0.0764372 | -0.2614769 | -0.2831098 | 0.5847920 | 0.5653687 | 0.3367834 | 0.1669174 |
| radius_se | 0.6790904 | 0.2758687 | 0.6917650 | 0.7325622 | 0.3014671 | 0.4974734 | 0.6319248 | 0.6980498 |
| texture_se | -0.0973174 | 0.3863576 | -0.0867611 | -0.0662802 | 0.0684064 | 0.0462048 | 0.0762183 | 0.0214796 |
| perimeter_se | 0.6741716 | 0.2816731 | 0.6931349 | 0.7266283 | 0.2960919 | 0.5489053 | 0.6603908 | 0.7106499 |
| area_se | 0.7358637 | 0.2598450 | 0.7449827 | 0.8000859 | 0.2465524 | 0.4556529 | 0.6174268 | 0.6902985 |
| smoothness_se | -0.2226001 | 0.0066138 | -0.2026940 | -0.1667767 | 0.3323754 | 0.1352993 | 0.0985637 | 0.0276533 |
| compactness_se | 0.2060000 | 0.1919746 | 0.2507437 | 0.2125826 | 0.3189433 | 0.7387218 | 0.6702788 | 0.4904242 |
| concavity_se | 0.1942036 | 0.1432931 | 0.2280823 | 0.2076601 | 0.2483957 | 0.5705169 | 0.6912702 | 0.4391671 |
| concave.points_se | 0.3761690 | 0.1638510 | 0.4072169 | 0.3723203 | 0.3806757 | 0.6422619 | 0.6832599 | 0.6156341 |
| symmetry_se | -0.1043209 | 0.0091272 | -0.0816293 | -0.0724966 | 0.2007744 | 0.2299766 | 0.1780092 | 0.0953508 |
| fractal_dimension_se | -0.0426413 | 0.0544575 | -0.0055234 | -0.0198870 | 0.2836067 | 0.5073181 | 0.4493007 | 0.2575837 |
| radius_worst | 0.9695390 | 0.3525729 | 0.9694764 | 0.9627461 | 0.2131201 | 0.5353154 | 0.6882364 | 0.8303176 |
| texture_worst | 0.2970076 | 0.9120446 | 0.3030384 | 0.2874886 | 0.0360718 | 0.2481328 | 0.2998789 | 0.2927517 |
| perimeter_worst | 0.9651365 | 0.3580396 | 0.9703869 | 0.9591196 | 0.2388526 | 0.5902104 | 0.7295649 | 0.8559231 |
| area_worst | 0.9410825 | 0.3435459 | 0.9415498 | 0.9592133 | 0.2067184 | 0.5096038 | 0.6759872 | 0.8096296 |
| smoothness_worst | 0.1196161 | 0.0775034 | 0.1505494 | 0.1235229 | 0.8053242 | 0.5655412 | 0.4488220 | 0.4527531 |
| compactness_worst | 0.4134628 | 0.2778296 | 0.4557742 | 0.3904103 | 0.4724684 | 0.8658090 | 0.7549680 | 0.6674537 |
| concavity_worst | 0.5269115 | 0.3010252 | 0.5638793 | 0.5126059 | 0.4349257 | 0.8162752 | 0.8841026 | 0.7523995 |
| concave.points_worst | 0.7442142 | 0.2953158 | 0.7712408 | 0.7220166 | 0.5030534 | 0.8155732 | 0.8613230 | 0.9101553 |
| symmetry_worst | 0.1639533 | 0.1050079 | 0.1891150 | 0.1435699 | 0.3943095 | 0.5102234 | 0.4094641 | 0.3757441 |
| fractal_dimension_worst | 0.0070659 | 0.1192054 | 0.0510185 | 0.0037376 | 0.4993164 | 0.6873823 | 0.5149299 | 0.3686611 |
| Variables altamente correl | adas: |
# find attributes that are highly corrected (ideally >0.75)
highlyCorrelated <- findCorrelation(correlationMatrix, cutoff=0.75)
# print indexes of highly correlated attributes
print(highlyCorrelated)## [1] 7 8 6 28 27 23 21 3 26 24 1 13 18 16 14 5 10 2# Fichero con las variables y una nueva columna que indica su eliminacion por predictor altamente correlado
expD3CorFind <-expD3Cor
expD3CorFind$Eliminada <- expD3CorFind$VariableOrigen %in% names(brc[highlyCorrelated])
CorCuantas <- expD3CorFind %>% group_by(Eliminada) %>% summarise(n=n())
CorCuantas## # A tibble: 2 x 2
## Eliminada n
## <lgl> <int>
## 1 FALSE 13
## 2 TRUE 17Los nombres de las variables mas correladas son:
print(names(brc[highlyCorrelated]))## [1] "compactness_mean" "concavity_mean" "smoothness_mean"
## [4] "concavity_worst" "compactness_worst" "texture_worst"
## [7] "fractal_dimension_se" "texture_mean" "smoothness_worst"
## [10] "perimeter_worst" "diagnosis" "texture_se"
## [13] "concavity_se" "smoothness_se" "perimeter_se"
## [16] "area_mean" "symmetry_mean" "radius_mean"3.5. Vamos a usar el algoritmo LVQ para determinar la importancia de las variables
# ensure results are repeatable
set.seed(7)
# prepare training scheme
control <- trainControl(method="repeatedcv", number=10, repeats=3)
# train the model
brc2 <- select(brc, -diagnosis)
brc2$diag = factor(brc$diag)
brc2 <- as.data.frame(brc2)
dim(brc2)## [1] 569 31summary(brc2)## radius_mean texture_mean perimeter_mean area_mean
## Min. : 6.981 Min. : 9.71 Min. : 43.79 Min. : 143.5
## 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17 1st Qu.: 420.3
## Median :13.370 Median :18.84 Median : 86.24 Median : 551.1
## Mean :14.127 Mean :19.29 Mean : 91.97 Mean : 654.9
## 3rd Qu.:15.780 3rd Qu.:21.80 3rd Qu.:104.10 3rd Qu.: 782.7
## Max. :28.110 Max. :39.28 Max. :188.50 Max. :2501.0
## smoothness_mean compactness_mean concavity_mean concave.points_mean
## Min. :0.05263 Min. :0.01938 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.08637 1st Qu.:0.06492 1st Qu.:0.02956 1st Qu.:0.02031
## Median :0.09587 Median :0.09263 Median :0.06154 Median :0.03350
## Mean :0.09636 Mean :0.10434 Mean :0.08880 Mean :0.04892
## 3rd Qu.:0.10530 3rd Qu.:0.13040 3rd Qu.:0.13070 3rd Qu.:0.07400
## Max. :0.16340 Max. :0.34540 Max. :0.42680 Max. :0.20120
## symmetry_mean fractal_dimension_mean radius_se texture_se
## Min. :0.1060 Min. :0.04996 Min. :0.1115 Min. :0.3602
## 1st Qu.:0.1619 1st Qu.:0.05770 1st Qu.:0.2324 1st Qu.:0.8339
## Median :0.1792 Median :0.06154 Median :0.3242 Median :1.1080
## Mean :0.1812 Mean :0.06280 Mean :0.4052 Mean :1.2169
## 3rd Qu.:0.1957 3rd Qu.:0.06612 3rd Qu.:0.4789 3rd Qu.:1.4740
## Max. :0.3040 Max. :0.09744 Max. :2.8730 Max. :4.8850
## perimeter_se area_se smoothness_se compactness_se
## Min. : 0.757 Min. : 6.802 Min. :0.001713 Min. :0.002252
## 1st Qu.: 1.606 1st Qu.: 17.850 1st Qu.:0.005169 1st Qu.:0.013080
## Median : 2.287 Median : 24.530 Median :0.006380 Median :0.020450
## Mean : 2.866 Mean : 40.337 Mean :0.007041 Mean :0.025478
## 3rd Qu.: 3.357 3rd Qu.: 45.190 3rd Qu.:0.008146 3rd Qu.:0.032450
## Max. :21.980 Max. :542.200 Max. :0.031130 Max. :0.135400
## concavity_se concave.points_se symmetry_se
## Min. :0.00000 Min. :0.000000 Min. :0.007882
## 1st Qu.:0.01509 1st Qu.:0.007638 1st Qu.:0.015160
## Median :0.02589 Median :0.010930 Median :0.018730
## Mean :0.03189 Mean :0.011796 Mean :0.020542
## 3rd Qu.:0.04205 3rd Qu.:0.014710 3rd Qu.:0.023480
## Max. :0.39600 Max. :0.052790 Max. :0.078950
## fractal_dimension_se radius_worst texture_worst perimeter_worst
## Min. :0.0008948 Min. : 7.93 Min. :12.02 Min. : 50.41
## 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08 1st Qu.: 84.11
## Median :0.0031870 Median :14.97 Median :25.41 Median : 97.66
## Mean :0.0037949 Mean :16.27 Mean :25.68 Mean :107.26
## 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72 3rd Qu.:125.40
## Max. :0.0298400 Max. :36.04 Max. :49.54 Max. :251.20
## area_worst smoothness_worst compactness_worst concavity_worst
## Min. : 185.2 Min. :0.07117 Min. :0.02729 Min. :0.0000
## 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720 1st Qu.:0.1145
## Median : 686.5 Median :0.13130 Median :0.21190 Median :0.2267
## Mean : 880.6 Mean :0.13237 Mean :0.25427 Mean :0.2722
## 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910 3rd Qu.:0.3829
## Max. :4254.0 Max. :0.22260 Max. :1.05800 Max. :1.2520
## concave.points_worst symmetry_worst fractal_dimension_worst diag
## Min. :0.00000 Min. :0.1565 Min. :0.05504 0:357
## 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146 1:212
## Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :0.29100 Max. :0.6638 Max. :0.20750model <- train(diag ~ ., data=brc2, method="lvq", preProcess="scale", trControl=control)
# estimate variable importance
importance <- varImp(model, scale=FALSE)
# summarize importance
print(importance)## ROC curve variable importance
##
## only 20 most important variables shown (out of 30)
##
## Importance
## perimeter_worst 0.9755
## radius_worst 0.9704
## area_worst 0.9698
## concave.points_worst 0.9667
## concave.points_mean 0.9644
## perimeter_mean 0.9469
## area_mean 0.9383
## concavity_mean 0.9378
## radius_mean 0.9375
## area_se 0.9264
## concavity_worst 0.9214
## perimeter_se 0.8764
## radius_se 0.8683
## compactness_mean 0.8638
## compactness_worst 0.8623
## concave.points_se 0.7918
## texture_worst 0.7846
## concavity_se 0.7808
## texture_mean 0.7758
## smoothness_worst 0.7541#Datos a exportar para d3.js( importancia sobre vae.objetivo)
expd3 <-importance$importance %>% select (correlacion = X0)
expd3$variable <- rownames(expd3)Representacion de las variables mas importantes respecto a la variable objetivo diag:
# plot importance
plot(importance)
## 3.6.Seleccion de variables usando el metodo RFE
# ensure the results are repeatable
set.seed(7)
# define the control using a random forest selection function
control <- rfeControl(functions=rfFuncs, method="cv", number=10)
# run the RFE algorithm
results <- rfe(brc2[,1:30], brc2[,31], sizes=c(1:30), rfeControl=control)
# summarize the results
print(results)##
## Recursive feature selection
##
## Outer resampling method: Cross-Validated (10 fold)
##
## Resampling performance over subset size:
##
## Variables Accuracy Kappa AccuracySD KappaSD Selected
## 1 0.8633 0.7049 0.05188 0.11050
## 2 0.9315 0.8530 0.03425 0.07490
## 3 0.9264 0.8415 0.04934 0.10848
## 4 0.9402 0.8720 0.02652 0.05534
## 5 0.9543 0.9033 0.03727 0.07695
## 6 0.9543 0.9027 0.02654 0.05448
## 7 0.9578 0.9099 0.02249 0.04713
## 8 0.9666 0.9284 0.01546 0.03280
## 9 0.9612 0.9172 0.01862 0.03897
## 10 0.9648 0.9251 0.02209 0.04646
## 11 0.9701 0.9360 0.01687 0.03593
## 12 0.9718 0.9399 0.01907 0.04068 *
## 13 0.9683 0.9325 0.01832 0.03872
## 14 0.9683 0.9325 0.01832 0.03872
## 15 0.9666 0.9289 0.02424 0.05114
## 16 0.9683 0.9325 0.02331 0.04935
## 17 0.9700 0.9362 0.02228 0.04707
## 18 0.9665 0.9286 0.01964 0.04134
## 19 0.9648 0.9251 0.02209 0.04646
## 20 0.9683 0.9325 0.01832 0.03872
## 21 0.9683 0.9323 0.02191 0.04635
## 22 0.9701 0.9360 0.02043 0.04360
## 23 0.9631 0.9210 0.02107 0.04472
## 24 0.9630 0.9208 0.01773 0.03711
## 25 0.9666 0.9287 0.02123 0.04482
## 26 0.9683 0.9324 0.02026 0.04267
## 27 0.9684 0.9324 0.02596 0.05528
## 28 0.9630 0.9209 0.01956 0.04123
## 29 0.9578 0.9096 0.01704 0.03600
## 30 0.9631 0.9209 0.01556 0.03234
##
## The top 5 variables (out of 12):
## area_worst, concave.points_worst, perimeter_worst, radius_worst, texture_worst# list the chosen features
predictors(results)## [1] "area_worst" "concave.points_worst" "perimeter_worst"
## [4] "radius_worst" "texture_worst" "concave.points_mean"
## [7] "area_se" "texture_mean" "concavity_worst"
## [10] "smoothness_worst" "concavity_mean" "area_mean"Representamos los resultados graficamente, precision usando cross validation
# plot the results
plot(results, type=c("g", "o"))
Del resultado de esta grafica podemos interpretar que las 12 variables mas correladas con la variable objetivo son el punto optimo para nuestro dataset de trabajo.
3.7.Análisis gráfico de las variables
Eliminamos las variables devueltas por findcorrelation y visualizamos las variables mas correladas:
cor.brc <- brc[,-highlyCorrelated]
pairs(cor.brc)
Análisis :perimeter_mean
brc_graph = brc
# distribucion normalizada
brc_graph_n = brc_n
brc_graph$diagCategorico <- ifelse(brc$diag == 1, "Maligno", "Benigno")
brc_graph_n$diagCategorico <- ifelse(brc_n$diag == 1, "Maligno", "Benigno")
library(ggplot2)
ggplot(brc_graph, aes(x = perimeter_mean)) + geom_histogram(binwidth = 1, fill = "green", colour = "black") + facet_grid(diagCategorico ~ .) + ggtitle ("Fig 1.1. Histograma perimeter_mean por tipo de tumor") + theme(plot.title=element_text(vjust = +1.5, size = 12))
Análisis: radius_worst
ggplot(brc_graph, aes(x = radius_worst)) + geom_histogram(binwidth = 1, fill = "red", colour = "black") + facet_grid(diagCategorico ~ .) + ggtitle ("Fig 1.2. Histograma radius_worst por tipo de tumor") + theme(plot.title=element_text(vjust = +1.5, size = 12))