Case Study : Identifying the Effective variables for Clustering Analysis using PCA.

Data Table:

df

Checking of Missing Vaue in Data Frame:

Distribution of Rules:

Principal Component Analysis :

So from Above plot we can take first four PC Component which is sufficient enougf to explain the variance in our Data.

pc <- prcomp(df.sc)
comp <- data.frame(pc$x[,1:4])
plot(comp,pch=16,col=rgb(0,0,0,0.5))

Loading Principal Component :

Loadings:
           Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10 Comp.11 Comp.12 Comp.13
VIB_RULE1  -0.236  0.457  0.253 -0.234 -0.181  0.175                      -0.109           0.725         
VIB_RULE2          0.434  0.437  0.128  0.425 -0.258  0.313 -0.301         0.242  -0.289  -0.134         
DE_RULE1   -0.299 -0.292        -0.297 -0.207 -0.220  0.345 -0.359  0.523 -0.312  -0.144                 
DE_RULE2   -0.370 -0.145               -0.229  0.176  0.188 -0.429 -0.298  0.555   0.373                 
NDE_RULE1  -0.365 -0.127         0.238  0.321                       0.117 -0.140   0.277           0.743 
NDE_RULE2  -0.355 -0.136  0.104  0.241  0.369        -0.130         0.186 -0.175   0.340          -0.666 
IDE_RULE2  -0.230  0.316 -0.457  0.144        -0.146  0.555  0.257 -0.354 -0.302                         
INDE_RULE2 -0.387                              0.141         0.582  0.277  0.478  -0.404                 
OIL_RULE1  -0.238               -0.375        -0.753 -0.363  0.132 -0.231  0.137                         
OIL_RULE2  -0.371 -0.168         0.161         0.161 -0.302 -0.247 -0.444 -0.271  -0.599                 
RULE3_1            0.326 -0.680  0.173  0.176        -0.336 -0.314  0.326  0.180           0.118         
VIB_RULE4   0.236 -0.464         0.248  0.251 -0.222  0.227        -0.102  0.173  -0.132   0.664         
Power                    -0.176 -0.668  0.589  0.368  0.112        -0.133                                

               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10 Comp.11 Comp.12 Comp.13
SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000   1.000   1.000   1.000   1.000
Proportion Var  0.077  0.077  0.077  0.077  0.077  0.077  0.077  0.077  0.077   0.077   0.077   0.077   0.077
Cumulative Var  0.077  0.154  0.231  0.308  0.385  0.462  0.538  0.615  0.692   0.769   0.846   0.923   1.000

Lets Check for Optimum No of Cluster: Within Sum of Square

wss <- (nrow(df.sc)-1)*sum(apply(df.sc , 2 , var))
for (i in 2:15)
 
  wss[i] <-   sum(kmeans(df.sc,centers = i)$withinss)
plot(1:15, wss,type="b",xlab=  "No of Cluster" , ylab = "Within Groups of sum of square",col="red",pch=16 , main="WSS by Cluster")
text(x=10, y=650,labels = "No Clear Elbow \nwe can Observe \n Within the Plot \n\n\n  Between 3 and 5 cluster is Optimium")

By Checking Within Group of Sum of Square we say that optimium K value should be either between 2 to 4 , Here in our case we will consider K=4

k <- kmeans(comp , 5 ,nstart = 25 , iter.max = 1000)
library(RColorBrewer) ; library(scales)
palette(alpha(brewer.pal(9,'Set1'),0.5))
plot(comp , col=k$clust,pch=16)

Cluster Size

sort(table(k$cluster))

 4  5  2  1  3 
 1  2 13 17 35 

clust <- names(sort(table(k$cluster)))

Turbines in Cluster-1

rownames(df[k$clust == clust[1],])

[1] "JMA173"

Turbines in Cluster-2

rownames(df[k$clust == clust[2],])

[1] "JMD511" "JMA174"

Turbines in Cluster-3

rownames(df[k$clust == clust[3],])

 [1] "JMA161" "JMA188" "JMD553" "JMA134" "JMA198" "JMA129" "JMD585" "JMA164" "JMA196" "JMA163" "JMA041" "JMA167" "JMA186"

Turbines in Cluster-4

rownames(df[k$clust == clust[4],])

 [1] "JMA183" "JMA182" "JMA053" "JMA133" "JMA195" "JMA102" "JMA105" "JMA165" "JMD563" "JMA187" "JMA216" "JMA197" "JMA203"
[14] "JMA044" "JMA103" "JMA189" "JMD338"

3D View of Clustering: PC1,PC2,PC3

library(rgl)
plot3d(comp$PC1,comp$PC2,comp$PC3,col=k$clust)

3D View of Clustering: PC1,PC3,PC4

library(rgl)
plot3d(comp$PC1,comp$PC3,comp$PC4,col=k$clust)
names(df)

 [1] "VIB_RULE1"  "VIB_RULE2"  "DE_RULE1"   "DE_RULE2"   "NDE_RULE1"  "NDE_RULE2"  "IDE_RULE1"  "IDE_RULE2"  "INDE_RULE1"
[10] "INDE_RULE2" "OIL_RULE1"  "OIL_RULE2"  "RULE3"      "RULE3_1"    "VIB_RULE4"  "OIL_RULE4"  "DE_RULE4"   "NDE_RULE4" 
[19] "IDE_RULE4"  "INDE_RULE4" "Power"     

Wind Turbine Accomodation By Cluster:

df.clus <-cbind(Cluster=k$cluster,df)
as.data.frame(df.clus)

names(df.clus)

 [1] "Cluster"    "VIB_RULE1"  "VIB_RULE2"  "DE_RULE1"   "DE_RULE2"   "NDE_RULE1"  "NDE_RULE2"  "IDE_RULE1"  "IDE_RULE2" 
[10] "INDE_RULE1" "INDE_RULE2" "OIL_RULE1"  "OIL_RULE2"  "RULE3"      "RULE3_1"    "VIB_RULE4"  "OIL_RULE4"  "DE_RULE4"  
[19] "NDE_RULE4"  "IDE_RULE4"  "INDE_RULE4" "Power"     

Classifying the Cluster:

library(rpart);library(partykit);library(rpart.plot);library(randomForest);library(rattle)
#res <- rpart(as.formula(paste(input$vars1," ~ ",paste(input$vars2,collapse="+"))),data=dat)
fit <- rpart(Cluster ~ ., data = df.clus)
fancyRpartPlot(fit)