ISLR Chapter 10 Lab 03 - NCI60 Data Example
p407
library(ISLR)Get Data
nci.labs=NCI60$labs
nci.data=NCI60$data
dim(nci.data) # 64 rows and 6,830 columns## [1] 64 6830Examine cancer types for the cell lines
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 1PCA on the NCI60 Data
pr.out=prcomp(nci.data, scale=TRUE)Function will be used to assign a color to each of the 64 cell lines, based on the cancer type to which it corresponds.
Cols=function(vec){
cols=rainbow(length(unique(vec)))
return(cols[as.numeric(as.factor(vec))])
}Plot the first few principal component score vectors
par(mfrow=c(1,2))
plot(pr.out$x[,1:2], col=Cols(nci.labs), pch=19, xlab="Z1", ylab="Z2")
plot(pr.out$x[,c(1,3)], col=Cols(nci.labs), pch=19, xlab="Z1", ylab="Z3")
On the whole, cell lines corresponding to a single cancer type do tend to have similar values on the first few principal component score vectors. summary of the proportion of variance explained (PVE)
Summary
summary(pr.out)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 27.8535 21.48136 19.82046 17.03256 15.97181 15.72108
## Proportion of Variance 0.1136 0.06756 0.05752 0.04248 0.03735 0.03619
## Cumulative Proportion 0.1136 0.18115 0.23867 0.28115 0.31850 0.35468
## PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 14.47145 13.54427 13.14400 12.73860 12.68672 12.15769
## Proportion of Variance 0.03066 0.02686 0.02529 0.02376 0.02357 0.02164
## Cumulative Proportion 0.38534 0.41220 0.43750 0.46126 0.48482 0.50646
## PC13 PC14 PC15 PC16 PC17 PC18
## Standard deviation 11.83019 11.62554 11.43779 11.00051 10.65666 10.48880
## Proportion of Variance 0.02049 0.01979 0.01915 0.01772 0.01663 0.01611
## Cumulative Proportion 0.52695 0.54674 0.56590 0.58361 0.60024 0.61635
## PC19 PC20 PC21 PC22 PC23 PC24
## Standard deviation 10.43518 10.3219 10.14608 10.0544 9.90265 9.64766
## Proportion of Variance 0.01594 0.0156 0.01507 0.0148 0.01436 0.01363
## Cumulative Proportion 0.63229 0.6479 0.66296 0.6778 0.69212 0.70575
## PC25 PC26 PC27 PC28 PC29 PC30 PC31
## Standard deviation 9.50764 9.33253 9.27320 9.0900 8.98117 8.75003 8.59962
## Proportion of Variance 0.01324 0.01275 0.01259 0.0121 0.01181 0.01121 0.01083
## Cumulative Proportion 0.71899 0.73174 0.74433 0.7564 0.76824 0.77945 0.79027
## PC32 PC33 PC34 PC35 PC36 PC37 PC38
## Standard deviation 8.44738 8.37305 8.21579 8.15731 7.97465 7.90446 7.82127
## Proportion of Variance 0.01045 0.01026 0.00988 0.00974 0.00931 0.00915 0.00896
## Cumulative Proportion 0.80072 0.81099 0.82087 0.83061 0.83992 0.84907 0.85803
## PC39 PC40 PC41 PC42 PC43 PC44 PC45
## Standard deviation 7.72156 7.58603 7.45619 7.3444 7.10449 7.0131 6.95839
## Proportion of Variance 0.00873 0.00843 0.00814 0.0079 0.00739 0.0072 0.00709
## Cumulative Proportion 0.86676 0.87518 0.88332 0.8912 0.89861 0.9058 0.91290
## PC46 PC47 PC48 PC49 PC50 PC51 PC52
## Standard deviation 6.8663 6.80744 6.64763 6.61607 6.40793 6.21984 6.20326
## Proportion of Variance 0.0069 0.00678 0.00647 0.00641 0.00601 0.00566 0.00563
## Cumulative Proportion 0.9198 0.92659 0.93306 0.93947 0.94548 0.95114 0.95678
## PC53 PC54 PC55 PC56 PC57 PC58 PC59
## Standard deviation 6.06706 5.91805 5.91233 5.73539 5.47261 5.2921 5.02117
## Proportion of Variance 0.00539 0.00513 0.00512 0.00482 0.00438 0.0041 0.00369
## Cumulative Proportion 0.96216 0.96729 0.97241 0.97723 0.98161 0.9857 0.98940
## PC60 PC61 PC62 PC63 PC64
## Standard deviation 4.68398 4.17567 4.08212 4.04124 2.148e-14
## Proportion of Variance 0.00321 0.00255 0.00244 0.00239 0.000e+00
## Cumulative Proportion 0.99262 0.99517 0.99761 1.00000 1.000e+00Plot the variance explained by the first few principal components
plot(pr.out, main="Variance Explained")
The height of each bar in the bar plot is given by squaring the corresponding element of pr.out$sdev.
It is more informative to plot the PVE of each principal component (i.e. a scree plot) and the cumulative PVE of each principal component.
pve=100*pr.out$sdev^2/sum(pr.out$sdev^2)
par(mfrow=c(1,2))
plot(pve, type="o", ylab="PVE", xlab="Principal Component", col =" blue ")
plot(cumsum(pve), type="o", ylab="Cumulative PVE", xlab="Principal Component ", col =" brown3 ")
Clustering the Observations of the NCI60 Data
this step is optional and should be performed only if we want each gene to be on the same scale.
sd.data=scale(nci.data)Perform hierarchical clustering of the observations using complete, single, and average linkage. Euclidean distance is used as the dissimilarity measure.
par(mfrow=c(3,1))
data.dist=dist(sd.data)
plot(hclust(data.dist), labels=nci.labs, main="Complete Linkage", xlab="", sub="",ylab="")
plot(hclust(data.dist, method="average"), labels=nci.labs, main="Average Linkage", xlab="", sub="",ylab="")
plot(hclust(data.dist, method="single"), labels=nci.labs, main="Single Linkage", xlab="", sub="",ylab="")
Complete and average linkage tend to yield evenly sized clusters whereas single linkage tends to yield extended clusters to which single leaves are fused one by one.
Cut height to 4
cut the dendrogram at the height that will yield a particular number of clusters
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 0All the leukemia cell lines fall in cluster 3, while the breast cancer cell lines are spread out over three different clusters.
Dendrogram
par(mfrow=c(1,1))
plot(hc.out, labels=nci.labs)
abline(h=139, col="red")
Printing the output of hclust gives a useful brief summary of the object
hc.out##
## Call:
## hclust(d = dist(sd.data))
##
## Cluster method : complete
## Distance : euclidean
## Number of objects: 64Commpare kmeans and hierarchical clustering
How do these NCI60 hierarchical clustering results compare to what we get if we perform K-means clustering with K = 4?
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 0We see that the four clusters obtained using hierarchical clustering and K-means clustering are somewhat different
Cluster 2 in K-means clustering is identical to cluster 3 in hierarchical clustering. However, the other clusters differ: for instance, cluster 4 in K-means clustering contains a portion of the observations assigned to cluster 1 by hierarchical clustering, as well as all of the observations assigned to cluster 2 by hierarchical clustering.
Perform hierarchical clustering on first few principal component score vectors
hc.out=hclust(dist(pr.out$x[,1:5]))
plot(hc.out, labels=nci.labs, main="Hier. Clust. on First Five Score Vectors")
table(cutree(hc.out,4), nci.labs)## nci.labs
## BREAST CNS COLON K562A-repro K562B-repro LEUKEMIA MCF7A-repro MCF7D-repro
## 1 0 2 7 0 0 2 0 0
## 2 5 3 0 0 0 0 0 0
## 3 0 0 0 1 1 4 0 0
## 4 2 0 0 0 0 0 1 1
## nci.labs
## MELANOMA NSCLC OVARIAN PROSTATE RENAL UNKNOWN
## 1 1 8 5 2 7 0
## 2 7 1 1 0 2 1
## 3 0 0 0 0 0 0
## 4 0 0 0 0 0 0