Poor results with only scale-type arguments in irlba and prcomp_irlba #21
Description
when I compare the results from the irlba package using the irlba function or prcomp_irlba and compare that to R's svd and prcomp functions, the results are usually quite good ('mean relative difference' on the order of 1e-7 or so as reported by all.equal). However, when using scale.=T or the sd's of the columns of the input matrix for scale in irlba(), the mean relative difference from the pca function is quite large, on the order of 0.1. When using center alone or with scale, the mean relative difference goes back to 1e-7 or so. Is this expected behavior?
I ran this on the latest git installed with install_github
Here is sample code, I left out the centered and scaled centered cases as those are working well
normalize_signs = function(X, Y) {
for (i in 1:ncol(X)) {
if (sign(X[1, i]) != sign(Y[1, i])) {
Y[,i] = -Y[,i]
}
}
return(Y)
}
all.equal_pca = function(X, Y) {
Y = normalize_signs(X, Y)
return(all.equal(X, Y, check.attributes=F))
}
set.seed(1)
X = matrix(rnorm(2000), ncol=40)
M = 5 # number of PCA components
centers = colMeans(X)
sds = apply(X, 2, sd)
Xc = sweep(X, 2, centers, `-`)
Xs = sweep(X, 2, sds, `/`)
Xcs = sweep(Xc, 2, sds, `/`)
# unscaled
scaled=F
centered=F
pca = prcomp(X, center=centered, scale.=scaled)
sv = svd(X)
svir = irlba(X, nv=M, nu=M)
pcair = prcomp_irlba(X, n=M, center=centered, scale.=scaled)
Xpca = predict(pca)[,1:M]
Xsvl = sv$u[,1:M] %*% diag(sv$d[1:M])
Xsvr = X %*% sv$v[,1:M]
Xsvirl = svir$u %*% diag(svir$d)
Xsvirr = X %*% svir$v
Xpcair = predict(pcair)
Xpcair2 = X %*% pcair$rotation
all.equal_pca(Xsvl, Xsvr)
all.equal_pca(Xpca, Xsvl)
all.equal_pca(Xsvirl, Xsvirr)
all.equal_pca(Xpca, Xsvirl)
all.equal_pca(Xpcair, Xpcair2)
all.equal_pca(Xpca, Xpcair)
all.equal_pca(Xpcair, Xsvirl)
# scaled, uncentered
scaled=T
centered=F
pca = prcomp(X, center=centered, scale.=scaled)
sv = svd(Xs)
svir = irlba(X, nv=M, nu=M, scale=sds)
pcair = prcomp_irlba(X, n=M, center=centered, scale.=scaled)
Xpca = predict(pca)[,1:M]
Xsvl = sv$u[,1:M] %*% diag(sv$d[1:M])
Xsvr = Xs %*% sv$v[,1:M]
Xsvirl = svir$u %*% diag(svir$d)
Xsvirr = Xs %*% svir$v
Xpcair = predict(pcair)
Xpcair2 = Xs %*% pcair$rotation
all.equal_pca(Xsvl, Xsvr)
all.equal_pca(Xpca, Xsvl)
all.equal_pca(Xsvirl, Xsvirr)
all.equal_pca(Xpca, Xsvirl)
all.equal_pca(Xpcair, Xpcair2)
all.equal_pca(Xpca, Xpcair)
all.equal_pca(Xpcair, Xsvirl)