Clusters

library(readr)
library(caret)
library(tidyverse)

kmeans

Intro

data(iris)
iris.new <- iris[,1:4]

set.seed(61)
cluster_col <- c("red","Blue", "Black")
km.iris <- kmeans(iris.new,centers = 3,nstart = 1)
plot(iris.new$Sepal.Length,iris.new$Sepal.Width,
     xlab = "Sepal Length",
     ylab = "Sepal Width",
     col = km.iris$cluster)
points(km.iris$centers,col= 1:3 , pch=8,cex=2)

wss <- 0
for (i in 1:15) {
  km.iris <- kmeans(iris.new, centers = i, nstart=20, iter.max = 50)
  wss[i] <- km.iris$tot.withinss
}
plot(1:15, wss, type = "b", 
     xlab = "Numero de Clusters", 
     ylab = "Suma de cuadrados entre grupos")

par(mfrow = c(2, 3))
# Set seed
set.seed(1)
for(i in 1:6) {
  # Run kmeans() on x with three clusters and one start
  km.mtcars <- kmeans(mtcars, 3, nstar=1,iter.max = 5)
  
  # Plot clusters
  plot(mtcars$wt,mtcars$qsec, col = km.mtcars$cluster, 
       main = km.mtcars$tot.withinss, 
       xlab = "", ylab = "")
}

Cancer

cancer <- read_csv("~/Dropbox/Cursos/fiabilidad/Material para la clase/clusters/data.csv")

dim(cancer)

[1] 569  33

names(cancer)

 [1] "id"                      "diagnosis"               "radius_mean"             "texture_mean"            "perimeter_mean"         
 [6] "area_mean"               "smoothness_mean"         "compactness_mean"        "concavity_mean"          "concave points_mean"    
[11] "symmetry_mean"           "fractal_dimension_mean"  "radius_se"               "texture_se"              "perimeter_se"           
[16] "area_se"                 "smoothness_se"           "compactness_se"          "concavity_se"            "concave points_se"      
[21] "symmetry_se"             "fractal_dimension_se"    "radius_worst"            "texture_worst"           "perimeter_worst"        
[26] "area_worst"              "smoothness_worst"        "compactness_worst"       "concavity_worst"         "concave points_worst"   
[31] "symmetry_worst"          "fractal_dimension_worst" NA                       

cancer.data <- cancer[,3:32]
diagnosis <- cancer[,2]
row.names(cancer.data) <- cancer[,1]
cancer.data

sum(is.na(cancer.data))

[1] 0

table(diagnosis)

diagnosis
  B   M 
357 212 

round(colMeans(cancer.data),3)

            radius_mean            texture_mean          perimeter_mean               area_mean         smoothness_mean        compactness_mean 
                 14.127                  19.290                  91.969                 654.889                   0.096                   0.104 
         concavity_mean     concave points_mean           symmetry_mean  fractal_dimension_mean               radius_se              texture_se 
                  0.089                   0.049                   0.181                   0.063                   0.405                   1.217 
           perimeter_se                 area_se           smoothness_se          compactness_se            concavity_se       concave points_se 
                  2.866                  40.337                   0.007                   0.025                   0.032                   0.012 
            symmetry_se    fractal_dimension_se            radius_worst           texture_worst         perimeter_worst              area_worst 
                  0.021                   0.004                  16.269                  25.677                 107.261                 880.583 
       smoothness_worst       compactness_worst         concavity_worst    concave points_worst          symmetry_worst fractal_dimension_worst 
                  0.132                   0.254                   0.272                   0.115                   0.290                   0.084 

round(apply(cancer.data,2,sd),3)

            radius_mean            texture_mean          perimeter_mean               area_mean         smoothness_mean        compactness_mean 
                  3.524                   4.301                  24.299                 351.914                   0.014                   0.053 
         concavity_mean     concave points_mean           symmetry_mean  fractal_dimension_mean               radius_se              texture_se 
                  0.080                   0.039                   0.027                   0.007                   0.277                   0.552 
           perimeter_se                 area_se           smoothness_se          compactness_se            concavity_se       concave points_se 
                  2.022                  45.491                   0.003                   0.018                   0.030                   0.006 
            symmetry_se    fractal_dimension_se            radius_worst           texture_worst         perimeter_worst              area_worst 
                  0.008                   0.003                   4.833                   6.146                  33.603                 569.357 
       smoothness_worst       compactness_worst         concavity_worst    concave points_worst          symmetry_worst fractal_dimension_worst 
                  0.023                   0.157                   0.209                   0.066                   0.062                   0.018 

cancer.data_impute <- preProcess(cancer.data,method = c("center","scale"))
cancer.data.cs <- predict(cancer.data_impute,cancer.data)

round(colMeans(cancer.data.cs),3)

            radius_mean            texture_mean          perimeter_mean               area_mean         smoothness_mean        compactness_mean 
                      0                       0                       0                       0                       0                       0 
         concavity_mean     concave points_mean           symmetry_mean  fractal_dimension_mean               radius_se              texture_se 
                      0                       0                       0                       0                       0                       0 
           perimeter_se                 area_se           smoothness_se          compactness_se            concavity_se       concave points_se 
                      0                       0                       0                       0                       0                       0 
            symmetry_se    fractal_dimension_se            radius_worst           texture_worst         perimeter_worst              area_worst 
                      0                       0                       0                       0                       0                       0 
       smoothness_worst       compactness_worst         concavity_worst    concave points_worst          symmetry_worst fractal_dimension_worst 
                      0                       0                       0                       0                       0                       0 

round(apply(cancer.data.cs,2,sd),3)

            radius_mean            texture_mean          perimeter_mean               area_mean         smoothness_mean        compactness_mean 
                      1                       1                       1                       1                       1                       1 
         concavity_mean     concave points_mean           symmetry_mean  fractal_dimension_mean               radius_se              texture_se 
                      1                       1                       1                       1                       1                       1 
           perimeter_se                 area_se           smoothness_se          compactness_se            concavity_se       concave points_se 
                      1                       1                       1                       1                       1                       1 
            symmetry_se    fractal_dimension_se            radius_worst           texture_worst         perimeter_worst              area_worst 
                      1                       1                       1                       1                       1                       1 
       smoothness_worst       compactness_worst         concavity_worst    concave points_worst          symmetry_worst fractal_dimension_worst 
                      1                       1                       1                       1                       1                       1 

km.out <- kmeans(cancer.data.cs,centers = 3, nstart =20)
summary(km.out)

             Length Class  Mode   
cluster      569    -none- numeric
centers       90    -none- numeric
totss          1    -none- numeric
withinss       3    -none- numeric
tot.withinss   1    -none- numeric
betweenss      1    -none- numeric
size           3    -none- numeric
iter           1    -none- numeric
ifault         1    -none- numeric

str(km.out)

List of 9
 $ cluster     : Named int [1:569] 1 1 1 3 1 3 1 3 3 3 ...
  ..- attr(*, "names")= chr [1:569] "842302" "842517" "84300903" "84348301" ...
 $ centers     : num [1:3, 1:30] 1.618 -0.448 -0.172 0.626 -0.242 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:3] "1" "2" "3"
  .. ..$ : chr [1:30] "radius_mean" "texture_mean" "perimeter_mean" "area_mean" ...
 $ totss       : num 17040
 $ withinss    : num [1:3] 2894 4358 2792
 $ tot.withinss: num 10044
 $ betweenss   : num 6996
 $ size        : int [1:3] 110 359 100
 $ iter        : int 3
 $ ifault      : int 0
 - attr(*, "class")= chr "kmeans"

wss <- 0
# For 1 to 15 cluster centers
for (i in 1:15) {
  km.out <- kmeans(cancer.data.cs, centers = i, nstart=20, iter.max = 50)
  # Save total within sum of squares to wss variable
  wss[i] <- km.out$tot.withinss
}
plot(1:15, wss, type = "b", 
     xlab = "Numero de Clusters", 
     ylab = "Suma de cuadrados entre grupos",main = "Scree Plot para el dataset de cancer de mamas")
points(2,wss[2],col = "red",pch = 16)

text(2,wss[2],labels = round(wss[2],2),cex = 0.7,pos = 4)

km.out <- kmeans(cancer.data.cs,centers = 2, nstart =30,iter.max = 30)
summary(km.out)

             Length Class  Mode   
cluster      569    -none- numeric
centers       60    -none- numeric
totss          1    -none- numeric
withinss       2    -none- numeric
tot.withinss   1    -none- numeric
betweenss      1    -none- numeric
size           2    -none- numeric
iter           1    -none- numeric
ifault         1    -none- numeric

cancer.data$cluster <- km.out$cluster
table(diagnosis,cancer.data$cluster)

         
diagnosis   1   2
        B  14 343
        M 175  37

cancer.data$p_diag <- ifelse(cancer.data$cluster == 1 ,"M","B")
confusionMatrix(cancer.data$p_diag,diagnosis,positive = "M")

Confusion Matrix and Statistics

          Reference
Prediction   B   M
         B 343  37
         M  14 175
                                          
               Accuracy : 0.9104          
                 95% CI : (0.8838, 0.9325)
    No Information Rate : 0.6274          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.804           
 Mcnemar's Test P-Value : 0.002066        
                                          
            Sensitivity : 0.8255          
            Specificity : 0.9608          
         Pos Pred Value : 0.9259          
         Neg Pred Value : 0.9026          
             Prevalence : 0.3726          
         Detection Rate : 0.3076          
   Detection Prevalence : 0.3322          
      Balanced Accuracy : 0.8931          
                                          
       'Positive' Class : M               
                                          

Hierarchical clustering

cancer.data.hc <- cancer[,3:32]
cancer.data.hc <- as.data.frame(cancer.data.hc)
diagnosis <- cancer[,2]
diagnosis_num <- as.numeric(diagnosis == "M") 
cancer.data.hc_impute <- preProcess(cancer.data.hc,method = c("center","scale"))
cancer.data.hc.cs <- predict(cancer.data_impute,cancer.data.hc)

cancer.data.hc.cs.dist <- dist(cancer.data.hc.cs)
cancer.hclust <- hclust(cancer.data.hc.cs.dist, method = "complete")
plot(cancer.hclust)
abline(h=19, col = "red")

cancer.hclust.cluster <- cutree(cancer.hclust, k=4)
table(cancer.hclust.cluster,diagnosis_num)

                     diagnosis_num
cancer.hclust.cluster   0   1
                    1  12 165
                    2   2   5
                    3 343  40
                    4   0   2

cancer.data.hc$pred <- ifelse(cancer.hclust.cluster %in% c(1,2,4), "M", "B")
confusionMatrix(cancer.data.hc$pred, diagnosis$diagnosis,positive = "M")

Confusion Matrix and Statistics

          Reference
Prediction   B   M
         B 343  40
         M  14 172
                                         
               Accuracy : 0.9051         
                 95% CI : (0.878, 0.9279)
    No Information Rate : 0.6274         
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.7918         
 Mcnemar's Test P-Value : 0.0006688      
                                         
            Sensitivity : 0.8113         
            Specificity : 0.9608         
         Pos Pred Value : 0.9247         
         Neg Pred Value : 0.8956         
             Prevalence : 0.3726         
         Detection Rate : 0.3023         
   Detection Prevalence : 0.3269         
      Balanced Accuracy : 0.8861         
                                         
       'Positive' Class : M              
                                         

Principal Component Analysis

cancer.data.pr <- cancer[,-c(1,2,33)]
cancer.pr <- prcomp(cancer.data.pr,scale = TRUE)
summary(cancer.pr)

Importance of components:
                          PC1    PC2     PC3     PC4     PC5     PC6     PC7     PC8    PC9    PC10   PC11    PC12    PC13    PC14
Standard deviation     3.6444 2.3857 1.67867 1.40735 1.28403 1.09880 0.82172 0.69037 0.6457 0.59219 0.5421 0.51104 0.49128 0.39624
Proportion of Variance 0.4427 0.1897 0.09393 0.06602 0.05496 0.04025 0.02251 0.01589 0.0139 0.01169 0.0098 0.00871 0.00805 0.00523
Cumulative Proportion  0.4427 0.6324 0.72636 0.79239 0.84734 0.88759 0.91010 0.92598 0.9399 0.95157 0.9614 0.97007 0.97812 0.98335
                          PC15    PC16    PC17    PC18    PC19    PC20   PC21    PC22    PC23   PC24    PC25    PC26    PC27    PC28
Standard deviation     0.30681 0.28260 0.24372 0.22939 0.22244 0.17652 0.1731 0.16565 0.15602 0.1344 0.12442 0.09043 0.08307 0.03987
Proportion of Variance 0.00314 0.00266 0.00198 0.00175 0.00165 0.00104 0.0010 0.00091 0.00081 0.0006 0.00052 0.00027 0.00023 0.00005
Cumulative Proportion  0.98649 0.98915 0.99113 0.99288 0.99453 0.99557 0.9966 0.99749 0.99830 0.9989 0.99942 0.99969 0.99992 0.99997
                          PC29    PC30
Standard deviation     0.02736 0.01153
Proportion of Variance 0.00002 0.00000
Cumulative Proportion  1.00000 1.00000

plot(cancer.pr)

biplot(cancer.pr)

plot(cancer.pr$x[, c(1, 2)], col=diagnosis_num+1, xlab = "PC1", ylab = "PC2")