MetaPCA implements simultaneous dimension reduction using Principal Component Analysis (PCA) when multiple studies are combined. We propose two basic ideas to find a common PC subspace by eigenvalue maximization approach and angle minimization approach, and we extend the concept to incorporate Robust PCA and Sparse PCA in the meta-analysis realm.
MetaPCA implements our proposed four methods to find common subspace among multiple studies (datasets):
- (1) Eigenvalue Maximization Approach
- (2) Angle Minimization Approach
- (3) Robust Angle Minimization Approach which extends Robust PCA
- (4) Sparse Angle Minimization Approach which extends Sparse PCA
For the detailed information, please see the references.
To install this package, save a proper package file for the target OS to the working directory, then run:
[MetaPCA_0.1.4.zip] (http://cran.r-project.org/bin/windows/contrib/r-release/MetaPCA_0.1.4.zip)
install.packages("MetaPCA_0.1.4.zip", repos=NULL, type="win.binary")
[MetaPCA_0.1.4.tgz] (http://cran.r-project.org/bin/macosx/leopard/contrib/r-release/MetaPCA_0.1.4.tgz)
install.packages("MetaPCA_0.1.4.tgz", repos=NULL, type="mac.binary")
[MetaPCA_0.1.4.tar.gz] (http://cran.r-project.org/src/contrib/MetaPCA_0.1.4.tar.gz)
install.packages("MetaPCA_0.1.4.tar.gz", repos=NULL, type="source")
library(MetaPCA)
requireAll("foreach")
#Spellman, 1998 Yeast cell cycle data set
#Consider each synchronization method as a separate data
data(Spellman)
pc <- list(alpha=prcomp(t(Spellman$alpha))$x, cdc15=prcomp(t(Spellman$cdc15))$x,
cdc28=prcomp(t(Spellman$cdc28))$x, elu=prcomp(t(Spellman$elu))$x)
#There are currently 4 meta-pca methods. Run either one of following four.
metaPC <- MetaPCA(Spellman, method="Eigen", doPreprocess=FALSE)
metaPC <- MetaPCA(Spellman, method="Angle", doPreprocess=FALSE)
metaPC <- MetaPCA(Spellman, method="RobustAngle", doPreprocess=FALSE)
metaPC <- MetaPCA(Spellman, method="SparseAngle", doPreprocess=FALSE)
#Comparing between usual pca and meta-pca
#The first lows are four data sets based on usual PCA, and
#the second rows are by MetaPCA
#We're looking for a cyclic pattern.
par(mfrow=c(2,4), cex=1, mar=c(0.2,0.2,0.2,0.2))
for(i in 1:4) {
plot(pc[[i]][,1], pc[[i]][,2], type="n", xlab="", ylab="", xaxt="n", yaxt="n")
text(pc[[i]][,1], pc[[i]][,2], 1:nrow(pc[[i]]), cex=1.5)
lines(pc[[i]][,1], pc[[i]][,2])
}
for(i in 1:4) {
plot(metaPC$x[[i]]$coord[,1], metaPC$x[[i]]$coord[,2], type="n", xlab="", ylab="", xaxt="n", yaxt="n")
text(metaPC$x[[i]]$coord[,1], metaPC$x[[i]]$coord[,2], 1:nrow(metaPC$x[[i]]$coord), cex=1.5)
lines(metaPC$x[[i]]$coord[,1], metaPC$x[[i]]$coord[,2])
}
#4 prostate cancer data which have three classes: normal, primary, metastasis
data(prostate)
#There are currently 4 meta-pca methods. Run either one of following four.
metaPC <- MetaPCA(prostate, method="Eigen", doPreprocess=FALSE, .scale=TRUE)
metaPC <- MetaPCA(prostate, method="Angle", doPreprocess=FALSE)
metaPC <- MetaPCA(prostate, method="RobustAngle", doPreprocess=FALSE)
metaPC <- MetaPCA(prostate, method="SparseAngle", doPreprocess=FALSE)
#Plotting 4 data in the same space!
coord <- foreach(dd=iter(metaPC$x), .combine=rbind) %do% dd$coord
PlotPC2D(coord[,1:2], drawEllipse=F, dataset.name="Prostate", .class.order=c("Metastasis","Primary","Normal"),
.class.color=c('red','#838383','blue'), .annotation=T, newPlot=T,
.class2=rep(names(metaPC$x), times=sapply(metaPC$x,function(x)nrow(x$coord))),
.class2.order=names(metaPC$x), .points.size=1)
#In the case of "SparseAngle" method, the top contributing genes for all studies can be determined
#For instance, top 20 genes in 1st PC and their coefficients
metaPC$v[order(abs(metaPC$v[,1]), decreasing=TRUE),1][1:20]
Dongwan D. Kang and George C. Tseng. (2011) Meta-PCA: Meta-analysis in the Dimension Reduction of Genomic data. (In preparation)