Hi Agus, >> But the rotation made with the eigenvectors of prcomp(X,center=F) yields >> axes that are correlated. Therefore, prcomp(X,center=F) is not really a >> PCA.
cor() is not an appropriate test of whether two vectors are orthogonal. The definition that two vectors (in an inner product space) are orthogonal is that their inner product is zero. ## The appropriate test uses ?"%*%" to multiply the matrices: set.seed(123) X <- cbind(rnorm(100,100,50),rnorm(100,100,50)) X[,2] <- X[,1]*1.5-50 +runif(100,-70,70) eigvcent <- prcomp(X,center=T,scaling=F) eigvnocent <- prcomp(X,center=F,scaling=F) eigvcent$rotation[,1] %*% eigvcent$rotation[,2] [1,] -2.211772e-17 eigvnocent$rotation[,1] %*% eigvnocent$rotation[,2] [1,] -1.680513e-17 In both cases, PCs 1 and 2 are orthogonal. Regards, Mark. alobo wrote: > > I do not understand, from a PCA point of view, the option center=F > of prcomp() > > According to the help page, the calculation in prcomp() "is done by a > singular value decomposition of the (centered and possibly scaled) data > matrix, not by using eigen on the covariance matrix" (as it's done by > princomp()) . > "This is generally the preferred method for numerical accuracy" > > The question is that while > prcomp(X,center=T,scaling=F) is equivalent to princomp(X,scaling=F), > but prcomp(X,center=F) has no equivalent in princomp() > > Also, the rotation made with either the eigenvectors of > prcomp(X,center=T,scaling=F) or the ones of princomp(X,scaling=F) > yields PCs with a minimum correlation, as expected > for a PCA. But the rotation made with the eigenvectors of > prcomp(X,center=F) yields axes that are correlated. > Therefore, prcomp(X,center=F) is not really a PCA. > > See the following example, in which the second column of > data matrix X is linearly correlated to the first column: > > > X <- cbind(rnorm(100,100,50),rnorm(100,100,50)) > > X[,2] <- X[,1]*1.5-50 +runif(100,-70,70) > > plot(X) > > cor(X[,1],X[,2]) > [1] 0.903597 > > > eigvnocent <- prcomp(X,center=F,scaling=F)[[1]] > > eigvcent <- prcomp(X,center=T,scaling=F)[[1]] > > eigvecnocent <- prcomp(X,center=F,scaling=F)[[2]] > > eigveccent <- prcomp(X,center=T,scaling=F)[[2]] > > > PCnocent <- X%*%eigvecnocent > > PCcent <- X%*%eigveccent > > par(mfrow=c(2,2)) > > plot(X) > > plot(PCnocent) > > plot(PCcent) > > > cor(X[,1],X[,2]) > [1] 0.903597 > > cor(PCcent[,1],PCcent[,2]) > [1] -8.778818e-16 > > cor(PCnocent[,1],PCnocent[,2]) > [1] -0.6908334 > > > > Also the help page of prcomp() states: > "Details > > The calculation is done by a singular value decomposition of the > (centered and possibly scaled) data matrix..." > > The parenthesis implies some ambiguity, but I do interpret the sentence > as indicating that the calculation should always be done using a > centered data matrix. > Finally, all the examples in the help page use centering (or scaling, > which implies centering) > > Therefore, why the option center=F ? > > Agus > > > > Agus > > -- > Dr. Agustin Lobo > Institut de Ciencies de la Terra "Jaume Almera" (CSIC) > LLuis Sole Sabaris s/n > 08028 Barcelona > Spain > Tel. 34 934095410 > Fax. 34 934110012 > email: agustin.l...@ija.csic.es > http://www.ija.csic.es/gt/obster > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- View this message in context: http://www.nabble.com/prcomp%28X%2Ccenter%3DF%29-----tp22396608p22397748.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
