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10.6 Lab 3: NCI60 Data Example 407 Correlation-based distance can be computed using the as.dist() func- as.dist() tion, which converts an arbitrary square symmetric matrix into a form that the hclust() function recognizes as a distance matrix. However, this only makes sense for data with at least three features since the absolute correlation between any two observations with measurements on two features is always 1. Hence, we will cluster a three-dimensional data set. > x=matrix(rnorm(30*3), ncol=3) > dd=as.dist(1-cor(t(x))) > plot(hclust(dd, method="complete "), main="Complete Linkage with Correlation -Based Distance", xlab="", sub="") 10.6 Lab 3: NCI60 Data Example Unsupervised techniques are often used in the analysis of genomic data. In particular, PCA and hierarchical clustering are popular tools. We illustrate these techniques on the NCI60 cancer cell line microarray data, which consists of 6,830 gene expression measurements on 64 cancer cell lines. > library(ISLR) > nci.labs=NCI60$labs > nci.data=NCI60$data Each cell line is labeled with a cancer type. We do not make use of the cancer types in performing PCA and clustering, as these are unsupervised techniques. But after performing PCA and clustering, we will check to see the extent to which these cancer types agree with the results of these unsupervised techniques. The data has 64 rows and 6,830 columns. > dim(nci.data) [1] 64 6830 We begin by examining the 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 7 5 7 1 1 LEUKEMIA MCF7A -repro MCF7D -repro MELANOMA NSCLC 6 1 1 8 9 OVARIAN PROSTATE RENAL UNKNOWN 6 2 9 1
408 10. Unsupervised Learning 10.6.1 PCA on the NCI60 Data We first perform PCA on the data after scaling the variables (genes) to have standard deviation one, although one could reasonably argue that it is better not to scale the genes. > pr.out=prcomp(nci.data, scale=TRUE) We now plot the first few principal component score vectors, in order to visualize the data. The observations (cell lines) corresponding to a given cancer type will be plotted in the same color, so that we can see to what extent the observations within a cancer type are similar to each other. We first create a simple function that assigns a distinct color to each element of a numeric vector. The 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))]) + } Note that the rainbow() function takes as its argument a positive integer, rainbow() and returns a vector containing that number of distinct colors. We now can plot the 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") The resulting plots are shown in Figure 10.15. 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. This indicates that cell lines from the same cancer type tend to have pretty similar gene expression levels. We can obtain a summary of the proportion of variance explained (PVE) of the first few principal components using the summary() method for a prcomp object (we have truncated the printout): > summary(pr.out) Importance of components : PC1 PC2 PC3 PC4 PC5 Standard deviation 27.853 21.4814 19.8205 17.0326 15.9718 Proportion of Variance 0.114 0.0676 0.0575 0.0425 0.0374 Cumulative Proportion 0.114 0.1812 0.2387 0.2812 0.3185 Using the plot() function, we can also plot the variance explained by the first few principal components. > plot(pr.out) Note that the height of each bar in the bar plot is given by squaring the corresponding element of pr.out$sdev. However, it is more informative to
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Springer Texts in Statistics Gareth
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Gareth James • Daniela Witten •
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To our parents: Alison and Michael
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viii Preface disciplines who wish t
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x Contents 3 Linear Regression 59 3
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3.6 Lab: Linear Regression 109 p=1
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3.6 Lab: Linear Regression 111 Coef
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4.2 Why Not Linear Regression? 129
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4.3 Logistic Regression 131 0 500 1
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4.3 Logistic Regression 133 β 1 do
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4.3 Logistic Regression 135 Coeffic
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9 Support Vector Machines In this c
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9.1 Maximal Margin Classifier 339 X
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Page 438 and 439: Index 423 noise, 22, 228 non-linear
Page 440 and 441: Index 425 read.table(), 48, 49 regs
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