The arrows are not pointing in the most-varying direction of the data. The principal components are pointing in the most-varying direction of the data. But you are not plotting the data on the original scale, you are plotting the data on the rotated scale, and thus the horizontal axis is the most-varying direction of the data.
The arrows are pointing in the direction of the variables, as projected into the 2-d plane of the biplot. There is no bug. Kevin Wright On Wed, Apr 25, 2012 at 11:29 AM, Michael <comtech....@gmail.com> wrote: > x=rmvnorm(2000, rep(0, 6), diag(c(5, rep(1,5)))) > x=scale(x, center=T, scale=F) > pc <- princomp(x) > biplot(pc) > > There are a bunch of red arrows plotted, what do they mean? I knew that the > first arrow labelled with "Var1" should be pointing the most varying > direction of the data-set (if we think them as 2000 data points, each being > a vector of size 6). I also read from somewhere, the most varying direction > should be the direction of the 1st eigen vector. > > However, reading into the code of biplot in R. The line about the arrows > is: > > if(var.axes) > arrows(0, 0, y[,1L] * 0.8, y[,2L] * 0.8, col = col[2L], > > Where `y` is the actually the loadings matrix, which is the eigenvector > matrix. So it looks like the 1st arrow is actually pointing from `(0, 0)` > to `(y[1, 1], y[1, 2])`. I understand that we are trying to plot a high > dimensional arrow onto a 2D plane. That's why we are taking the 1st and 2nd > element of the `y[1, ]` vector. However what I don't understand is: > > Shouldn't the 1st eigenvector direction be the vector denoted by `y[, 1]`, > instead of `y[1, ]`? (Again, here `y` is the eigenvector matrix, obtained > by PCA or by eigendecomposition of `t(x) %*% x`.) i.e. the eigenvectors > should be column vectors, not those horizontal vectors. > > Even though we are plotting them on 2D plane, we should draw the 1st > direction to be from `(0, 0)` pointing to `(y[1, 1], y[2, 1])`? > > > > I think the R code biplot.princomp has a bug: the loading matrix > (eigenvector matrix) should be transposed before being sent into > biplot.princomp... Any thoughts? > > [[alternative HTML version deleted]] > > ______________________________________________ > 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. > -- Kevin Wright [[alternative HTML version deleted]] ______________________________________________ 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.
