p407

``library(ISLR)``

Get Data

``````nci.labs=NCI60\$labs
nci.data=NCI60\$data
dim(nci.data) # 64 rows and 6,830 columns``````
``## [1]   64 6830``

Examine 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           1``````

PCA 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+00``````

Plot 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.Â 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 ")``````