OBJECTIVE:

Using the clustering method to “NCI60”(cancer cell line microarray) data, with the goal of finding out whether or not the observations cluster into the distinct types of cancer. A comparison between K_means and hierarchical clustering.

#NCI60 data set info
library(ISLR)
nci.labs=NCI60$labs
nci.data=NCI60$data
dim(nci.data)
## [1]   64 6830
nci.labs[1:4]
## [1] "CNS"   "CNS"   "CNS"   "RENAL"
table(nci.labs)
## nci.labs
##      BREAST         CNS       COLON K562A-repro K562B-repro    LEUKEMIA 
##           7           5           7           1           1           6 
## MCF7A-repro MCF7D-repro    MELANOMA       NSCLC     OVARIAN    PROSTATE 
##           1           1           8           9           6           2 
##       RENAL     UNKNOWN 
##           9           1
nci.labs
##  [1] "CNS"         "CNS"         "CNS"         "RENAL"       "BREAST"     
##  [6] "CNS"         "CNS"         "BREAST"      "NSCLC"       "NSCLC"      
## [11] "RENAL"       "RENAL"       "RENAL"       "RENAL"       "RENAL"      
## [16] "RENAL"       "RENAL"       "BREAST"      "NSCLC"       "RENAL"      
## [21] "UNKNOWN"     "OVARIAN"     "MELANOMA"    "PROSTATE"    "OVARIAN"    
## [26] "OVARIAN"     "OVARIAN"     "OVARIAN"     "OVARIAN"     "PROSTATE"   
## [31] "NSCLC"       "NSCLC"       "NSCLC"       "LEUKEMIA"    "K562B-repro"
## [36] "K562A-repro" "LEUKEMIA"    "LEUKEMIA"    "LEUKEMIA"    "LEUKEMIA"   
## [41] "LEUKEMIA"    "COLON"       "COLON"       "COLON"       "COLON"      
## [46] "COLON"       "COLON"       "COLON"       "MCF7A-repro" "BREAST"     
## [51] "MCF7D-repro" "BREAST"      "NSCLC"       "NSCLC"       "NSCLC"      
## [56] "MELANOMA"    "BREAST"      "BREAST"      "MELANOMA"    "MELANOMA"   
## [61] "MELANOMA"    "MELANOMA"    "MELANOMA"    "MELANOMA"
sd.data=scale(nci.data) # standardized the variables (mean zero and standard deviation one).

Comparison between complete, average and single linkage.

par(mfrow=c(1,1))
data.dist = dist(sd.data)
plot(hclust(data.dist),labels=nci.labs,main="Complete Linkage",
xlab="",sub="",ylab = "",cex=".5",col="blue") #Hierarchical clustering of the observations using Complete Linkage.

par(mfrow=c(1,1)) 
plot(hclust(data.dist,method="average"),labels=nci.labs,main="AverageLinkage",
xlab="",sub="",ylab = "",cex=".5",col="blue") #Hierarchical clustering of the observations using Average linkage.

par(mfrow=c(1,1))
plot(hclust(data.dist,method="single"),labels=nci.labs,main="SingleLinkage",
xlab="",sub="",ylab= "",cex=".5",col="blue") #Hierarchical clustering of the observations using Single Linkage.

OBSERVATIONS:

Single clusters tend to yield trailing clusters: very large clusters into which individual observations attached one by one.

On the other hand, complete and average linkage tends to yield more balanced and attractive clusters.

For this reason complete and average linkage are preferred to single linkage. Cell lines within a single cancer type do tend to cluster together, although the clustering is not perfect.

hc.out=hclust(dist(sd.data))
hc.clusters=cutree(hc.out,4)
table(hc.clusters,nci.labs)
##            nci.labs
## hc.clusters BREAST CNS COLON K562A-repro K562B-repro LEUKEMIA MCF7A-repro
##           1      2   3     2           0           0        0           0
##           2      3   2     0           0           0        0           0
##           3      0   0     0           1           1        6           0
##           4      2   0     5           0           0        0           1
##            nci.labs
## hc.clusters MCF7D-repro MELANOMA NSCLC OVARIAN PROSTATE RENAL UNKNOWN
##           1           0        8     8       6        2     8       1
##           2           0        0     1       0        0     1       0
##           3           0        0     0       0        0     0       0
##           4           1        0     0       0        0     0       0

We can see a clear pattern that all the leukemia cell lines fall under cluster 3 where the breast cancer cells are spread out over three different cluster.

plot(hc.out,labels=nci.labs,main="Cluster Dendrogram",xlab="",sub="",ylab = "",cex=".5", col="25",cex=".5")
abline(h=139, col="red")

The argument h=139 plot a horizontal line at height 139. This is the height result in 4 distinct clustering.

hc.out 
## 
## Call:
## hclust(d = dist(sd.data))
## 
## Cluster method   : complete 
## Distance         : euclidean 
## Number of objects: 64
set.seed(2)
km.out=kmeans(sd.data,4,nstart=20)
km.clusters=km.out$cluster
table(km.clusters,hc.clusters)
##            hc.clusters
## km.clusters  1  2  3  4
##           1 11  0  0  9
##           2 20  7  0  0
##           3  9  0  0  0
##           4  0  0  8  0

We see that the four clusters obtaining hierarchical clustering and K-means clustering are yielding different results. Cluster 2 in K-means clustering is identical to cluster 3 in hierarchical clustering. on the other hand the other clusters are differ.

CONCLUSION:

Hierarchical clustering performs better clustering in NCI60 data set instead of K-means