K-mean cluster using Wine dataset

This wine dataset is a result of chemical analysis of wines grown in a particular area. The analysis determined the quantities of 13 constituents found in each of the three types of wines. The attributes are: Alcohol, Malic acid, Ash, Alkalinity of ash, Magnesium, Total phenols, Flavonoids, Non-Flavonoid phenols, Proanthocyanins, Color intensity, Hue, OD280/OD315 of diluted wines, and Proline. The data set has 178 observations and no missing values.

Load thedata set

Wine <- read.csv("file:///C:/Users/badal/Desktop/datset_/Wine.csv") 
head(Wine)

str(Wine)

'data.frame':   178 obs. of  14 variables:
 $ Alcohol             : num  14.2 13.2 13.2 14.4 13.2 ...
 $ Malic_Acid          : num  1.71 1.78 2.36 1.95 2.59 1.76 1.87 2.15 1.64 1.35 ...
 $ Ash                 : num  2.43 2.14 2.67 2.5 2.87 2.45 2.45 2.61 2.17 2.27 ...
 $ Ash_Alcanity        : num  15.6 11.2 18.6 16.8 21 15.2 14.6 17.6 14 16 ...
 $ Magnesium           : int  127 100 101 113 118 112 96 121 97 98 ...
 $ Total_Phenols       : num  2.8 2.65 2.8 3.85 2.8 3.27 2.5 2.6 2.8 2.98 ...
 $ Flavanoids          : num  3.06 2.76 3.24 3.49 2.69 3.39 2.52 2.51 2.98 3.15 ...
 $ Nonflavanoid_Phenols: num  0.28 0.26 0.3 0.24 0.39 0.34 0.3 0.31 0.29 0.22 ...
 $ Proanthocyanins     : num  2.29 1.28 2.81 2.18 1.82 1.97 1.98 1.25 1.98 1.85 ...
 $ Color_Intensity     : num  5.64 4.38 5.68 7.8 4.32 6.75 5.25 5.05 5.2 7.22 ...
 $ Hue                 : num  1.04 1.05 1.03 0.86 1.04 1.05 1.02 1.06 1.08 1.01 ...
 $ OD280               : num  3.92 3.4 3.17 3.45 2.93 2.85 3.58 3.58 2.85 3.55 ...
 $ Proline             : int  1065 1050 1185 1480 735 1450 1290 1295 1045 1045 ...
 $ Customer_Segment    : int  1 1 1 1 1 1 1 1 1 1 ...

summary(Wine)

    Alcohol        Malic_Acid         Ash         Ash_Alcanity     Magnesium      Total_Phenols     Flavanoids   
 Min.   :11.03   Min.   :0.740   Min.   :1.360   Min.   :10.60   Min.   : 70.00   Min.   :0.980   Min.   :0.340  
 1st Qu.:12.36   1st Qu.:1.603   1st Qu.:2.210   1st Qu.:17.20   1st Qu.: 88.00   1st Qu.:1.742   1st Qu.:1.205  
 Median :13.05   Median :1.865   Median :2.360   Median :19.50   Median : 98.00   Median :2.355   Median :2.135  
 Mean   :13.00   Mean   :2.336   Mean   :2.367   Mean   :19.49   Mean   : 99.74   Mean   :2.295   Mean   :2.029  
 3rd Qu.:13.68   3rd Qu.:3.083   3rd Qu.:2.558   3rd Qu.:21.50   3rd Qu.:107.00   3rd Qu.:2.800   3rd Qu.:2.875  
 Max.   :14.83   Max.   :5.800   Max.   :3.230   Max.   :30.00   Max.   :162.00   Max.   :3.880   Max.   :5.080  
 Nonflavanoid_Phenols Proanthocyanins Color_Intensity       Hue             OD280          Proline      
 Min.   :0.1300       Min.   :0.410   Min.   : 1.280   Min.   :0.4800   Min.   :1.270   Min.   : 278.0  
 1st Qu.:0.2700       1st Qu.:1.250   1st Qu.: 3.220   1st Qu.:0.7825   1st Qu.:1.938   1st Qu.: 500.5  
 Median :0.3400       Median :1.555   Median : 4.690   Median :0.9650   Median :2.780   Median : 673.5  
 Mean   :0.3619       Mean   :1.591   Mean   : 5.058   Mean   :0.9574   Mean   :2.612   Mean   : 746.9  
 3rd Qu.:0.4375       3rd Qu.:1.950   3rd Qu.: 6.200   3rd Qu.:1.1200   3rd Qu.:3.170   3rd Qu.: 985.0  
 Max.   :0.6600       Max.   :3.580   Max.   :13.000   Max.   :1.7100   Max.   :4.000   Max.   :1680.0  
 Customer_Segment
 Min.   :1.000   
 1st Qu.:1.000   
 Median :2.000   
 Mean   :1.938   
 3rd Qu.:3.000   
 Max.   :3.000   

any(is.na(Wine))

[1] FALSE

Wine_scale <- scale(Wine[-1]) 
dim(Wine_scale)

[1] 178  13

head(Wine_scale,3)

      Malic_Acid        Ash Ash_Alcanity  Magnesium Total_Phenols Flavanoids Nonflavanoid_Phenols Proanthocyanins
[1,] -0.56066822  0.2313998   -1.1663032 1.90852151     0.8067217  1.0319081           -0.6577078       1.2214385
[2,] -0.49800856 -0.8256672   -2.4838405 0.01809398     0.5670481  0.7315653           -0.8184106      -0.5431887
[3,]  0.02117152  1.1062139   -0.2679823 0.08810981     0.8067217  1.2121137           -0.4970050       2.1299594
     Color_Intensity       Hue     OD280   Proline Customer_Segment
[1,]       0.2510088 0.3611585 1.8427215 1.0101594        -1.210529
[2,]      -0.2924962 0.4049085 1.1103172 0.9625263        -1.210529
[3,]       0.2682629 0.3174085 0.7863692 1.3912237        -1.210529

library(cluster)
library(factoextra)
library(ggplot2)

A fundamental question is how to determine the value of the parameter

. If we looks at the percentage of variance explained as a function of the number of clusters: One should choose a number of clusters so that adding another cluster doesn’t give much better modeling of the data. More precisely, if one plots the percentage of variance explained by the clusters against the number of clusters, the first clusters will add much information (explain a lot of variance), but at some point the marginal gain will drop, giving an angle in the graph. The number of clusters is chosen at this point, hence the “elbow criterion”.

wssplot <- function(data, nc=15, seed=1234){
  wss <- (nrow(data)-1)*sum(apply(data,2,var))
  for (i in 2:nc){
    set.seed(seed)
    wss[i] <- sum(kmeans(data, centers=i)$withinss)}
  plot(1:nc, wss, type="b", xlab="Number of Clusters",
       ylab="Within groups sum of squares")}
wssplot(Wine_scale, nc=10)

fviz_nbclust(Wine_scale, kmeans, method = 'wss') +
             geom_vline(xintercept =3, linetype=5, col= "darkred")

K-Means

k.means <- kmeans(Wine_scale, 3,nstart = 25) # k = 4
k.means

K-means clustering with 3 clusters of sizes 61, 49, 68

Cluster means:
  Malic_Acid        Ash Ash_Alcanity   Magnesium Total_Phenols  Flavanoids Nonflavanoid_Phenols Proanthocyanins
1 -0.3496504 -0.4749050    0.1821600 -0.63500454    -0.1786906 -0.03931453           0.09838569      -0.1419158
2  0.9024258  0.2485092    0.5820616 -0.05049296    -0.9857762 -1.23271740           0.71482528      -0.7474990
3 -0.3366204  0.2469449   -0.5828349  0.60602106     0.8706347  0.92354910          -0.60335244       0.6659457
  Color_Intensity        Hue      OD280    Proline Customer_Segment
1      -0.8885415  0.4498060  0.2139764 -0.8242592       0.07973544
2       0.9857177 -1.1879477 -1.2978785 -0.3789756       1.34366784
3       0.0867774  0.4525187  0.7432866  1.0124943      -1.03975861

Clustering vector:
  [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
 [57] 3 3 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 3 1 1 1 3 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1
[113] 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[169] 2 2 2 2 2 2 2 2 2 2

Within cluster sum of squares by cluster:
[1] 451.3039 284.5561 459.7529
 (between_SS / total_SS =  48.0 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"        
[8] "iter"         "ifault"      

# Centroids:
k.means$centers

  Malic_Acid        Ash Ash_Alcanity   Magnesium Total_Phenols  Flavanoids Nonflavanoid_Phenols Proanthocyanins
1 -0.3496504 -0.4749050    0.1821600 -0.63500454    -0.1786906 -0.03931453           0.09838569      -0.1419158
2  0.9024258  0.2485092    0.5820616 -0.05049296    -0.9857762 -1.23271740           0.71482528      -0.7474990
3 -0.3366204  0.2469449   -0.5828349  0.60602106     0.8706347  0.92354910          -0.60335244       0.6659457
  Color_Intensity        Hue      OD280    Proline Customer_Segment
1      -0.8885415  0.4498060  0.2139764 -0.8242592       0.07973544
2       0.9857177 -1.1879477 -1.2978785 -0.3789756       1.34366784
3       0.0867774  0.4525187  0.7432866  1.0124943      -1.03975861

# Clusters:
k.means$cluster

  [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
 [57] 3 3 3 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 3 1 1 1 3 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1
[113] 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[169] 2 2 2 2 2 2 2 2 2 2

Determining cluster size that is, the number of points in each cluster.

# Cluster size:
k.means$size

[1] 61 49 68

2D representation of clusters

clusplot(Wine_scale, k.means$cluster, main='2D representation of the Cluster',
         color=TRUE, shade=TRUE,
         labels=2, lines=0)

fviz_cluster(object = k.means, # kmeans object 
             data = Wine_scale, # data used for clustering
             ellipse.type = "norm",
             geom = "point",
             palette = "jco",
             main = "",
             ggtheme = theme_minimal())

The optimal number of clusters that are 3 in numbers and visualize K-mean clustering.