PCA clearly explained

Update: A lot of people ask to see example code that shows how to actually do PCA. Here’s how to do it in R

[sourcecode language=”R”]
## In this example, the data is in a matrix called
## data.matrix
## columns are individual samples (i.e. cells)
## rows are measurements taken for all the samples (i.e. genes)
## Just for the sake of the example, here’s some made up data…
data.matrix <- matrix(nrow=100, ncol=10)
colnames(data.matrix) <- c(
paste("wt", 1:5, sep=""),
paste("ko", 1:5, sep=""))
rownames(data.matrix) <- paste("gene", 1:100, sep="")
for (i in 1:100) {
wt.values <- rpois(5, lambda=sample(x=10:1000, size=1))
ko.values <- rpois(5, lambda=sample(x=10:1000, size=1))

data.matrix[i,] <- c(wt.values, ko.values)

pca <- prcomp(t(data.matrix), scale=TRUE)

## plot pc1 and pc2
plot(pca$x[,1], pca$x[,2])

## get the name of the sample (cell) with the highest pc1 value
rownames(pca$x)[order(pca$x[ ,1], decreasing=TRUE)[1]]

## get the name of the top 10 measurements (genes) that contribute
## most to pc1.
loading_scores <- pca$rotation[,1]
gene_scores <- abs(loading_scores) ## get the magnitudes
gene_score_ranked <- sort(gene_scores, decreasing=TRUE)
top_10_genes <- names(gene_score_ranked[1:10])

top_10_genes ## show the names of the top 10 genes

## get the scree information
pca.var <- pca$sdev^2
scree <- pca.var/sum(pca.var)
plot((scree[1:10]*100), main="Scree Plot", xlab="Principal Component", ylab="Percent Variation")

RNA-seq results often contain a PCA (Principal Component Analysis) or MDS plot. Usually we use these graphs to verify that the control samples cluster together. However, there’s a lot more going on, and if you are willing to dive in, you can extract a lot more information from these plots. The good news is that PCA only sounds complicated. Conceptually, it’s actually quite simple.

In this video I clearly explain how PCA graphs are generated, how to interpret them, and how to determine if the plot is informative or not. I then show how you can extract extra information out of the data used to draw the graph.