I regularly use a biplot or principal components plot as an initial exploratory tool for microarray analyses, but I have not found a good package that does this for me automatically. Rather than re-inventing the code every time, I created a simple R function that does the job for me. It’s not the fanciest or best code in the world, but I wanted to put it here and comment on the various alternative forms of the biplot and principal components plot when I have time.
pc.plot <- function(x,ulabs,vlabs) { <U+FFFD>nrows <- dim(x)[[1]] <U+FFFD>ncols <- dim(x)[[2]] <U+FFFD>x.means <- apply(x,1,mean) <U+FFFD>x.sd <- sqrt(apply(x,1,var)) <U+FFFD>x.cen <- x - (x.means %o% rep(1,ncols)) <U+FFFD>x.z <- x.cen / (x.sd %o% rep(1,ncols)) <U+FFFD>x.svd <- svd(x.z) <U+FFFD>d1 <- x.svd$d[1] <U+FFFD>d2 <- x.svd$d[2] <U+FFFD>u1 <- x.svd$u[,1]*sqrt(d1) <U+FFFD>u2 <- x.svd$u[,2]*sqrt(d2) <U+FFFD>v1 <- x.svd$v[,1]*sqrt(d1) <U+FFFD>v2 <- x.svd$v[,2]*sqrt(d2) <U+FFFD>u.v.range <- range(u1,u2,v1,v2) <U+FFFD>par(mar=rep(0.1,4)) <U+FFFD>plot(u.v.range,u.v.range,type="n",xlab=" ",ylab=" ") <U+FFFD>arrows(0,0,v1,v2) <U+FFFD>text(v1,v2,vlabs) <U+FFFD>text(u1,u2,steroid.symbol) <U+FFFD>u1 }
This code uses the singular value decomposition function (svd) to identify the linear combinations of rows and columns that maximize the variation. There are several scaling options that I could choose that will give different perspectives on this plot. Also, the ulabs argument provides labels for each row of X, which may be impractical for many large scale problems.
An article I commented on in the weblog entry,
- The Journal of Statistical Software (January 18, 2006)
provides some valuable comments about biplots, though it uses a different program for its examples.
- Interactive Biplot Construction. Udina F. Journal of Statistical Software 2005: 13(5); [PDF]