> dim(train)
[1]  33 102
> unique(train[,1])
[1] Crete      Peloponese Other
Levels: Crete Other Peloponese

> train.pca <- prcomp(train[,-1],center = TRUE,scale. = TRUE)
> summary(train.pca)
Importance of components:
                          PC1    PC2    PC3    PC4     PC5    PC6     PC7    PC8     PC9    PC10    PC11
Standard deviation     6.2499 5.5934 4.3538 2.5857 1.53128 1.1457 0.88391 0.5223 0.37085 0.27148 0.20914
Proportion of Variance 0.3867 0.3098 0.1877 0.0662 0.02322 0.0130 0.00774 0.0027 0.00136 0.00073 0.00043
Cumulative Proportion  0.3867 0.6965 0.8842 0.9504 0.97360 0.9866 0.99433 0.9970 0.99840 0.99912 0.99956
                          PC12    PC13    PC14    PC15    PC16    PC17    PC18    PC19    PC20    PC21
Standard deviation     0.10622 0.09947 0.07317 0.06188 0.05741 0.04700 0.04026 0.03675 0.03154 0.03029
Proportion of Variance 0.00011 0.00010 0.00005 0.00004 0.00003 0.00002 0.00002 0.00001 0.00001 0.00001
Cumulative Proportion  0.99967 0.99977 0.99982 0.99986 0.99989 0.99991 0.99993 0.99994 0.99995 0.99996
                          PC22    PC23    PC24    PC25    PC26    PC27    PC28    PC29    PC30    PC31
Standard deviation     0.02676 0.02422 0.02301 0.01986 0.01969 0.01836 0.01757 0.01506 0.01304 0.01241
Proportion of Variance 0.00001 0.00001 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
Cumulative Proportion  0.99997 0.99997 0.99998 0.99998 0.99999 0.99999 0.99999 1.00000 1.00000 1.00000
                          PC32      PC33
Standard deviation     0.01016 3.344e-13
Proportion of Variance 0.00000 0.000e+00
Cumulative Proportion  1.00000 1.000e+00

validation.pca <- predict(train.pca,newdata = validation[,-1])

> set.seed(1234)
> #tune k using transformed data
> ccr.tnx <-numeric(25)
> for(j in 1:25)
+ {
+   pred.class.tnx<-knn(train.pca$x[,1:4],
+                   validation.pca[,1:4],
+                   train[,1],
+                   k=j)
+   ccr.tnx[j]<-sum((pred.class.tnx==validation[,1]))/length(pred.class.tnx)
+   print(ccr.tnx[j])
+ }
[1] 0.8823529
[1] 0.8823529
[1] 0.7058824
[1] 0.8235294
[1] 0.8235294
[1] 0.8235294
[1] 0.6470588
[1] 0.7647059
[1] 0.7058824
[1] 0.6470588
[1] 0.8235294
[1] 0.7647059
[1] 0.7647059
[1] 0.7058824
[1] 0.7647059
[1] 0.6470588
[1] 0.6470588
[1] 0.7647059
[1] 0.7647059
[1] 0.7058824
[1] 0.6470588
[1] 0.5882353
[1] 0.5294118
[1] 0.7058824
[1] 0.7058824

> ccr.tnx[2]
[1] 0.8823529

> set.seed(1234)
> pred.class.tnx.2<-knn(train.pca$x[,1:4],
+                     validation.pca[,1:4],
+                     train[,1],
+                     k=2)
> sum((pred.class.tnx.2==validation[,1]))/length(pred.class.tnx.2)
[1] 0.6470588