Incorrect eigenvalue normalization for SVD-PCA

[r-de-r]

loadings is different between method==:svd and method==:var

[wildart]

Why would they be different? Eigenvalues from SVD are stored in formalized form.

[r-de-r]

2022/02/14 12:24、Art ***@***.***>のメール: Why would they be different? Eigenvalues from SVD are stored in formalized form. — Reply to this email directly, view it on GitHub, or unsubscribe. Triage notifications on the go with GitHub Mobile for iOS or Android. You are receiving this because you authored the thread.

I don't know why. Followings are results. julia> using MultivariateStats julia> using RDatasets julia> iris = RDatasets.dataset("datasets", "iris"); julia> x = Matrix(iris[:, 1:4])'; julia> M_cov = fit(PCA, x, method=:cov) PCA(indim = 4, outdim = 3, principalratio = 0.9947878161267246) julia> loadings(M_cov) 4×3 Matrix{Float64}: -0.743108 0.323446 0.16277 0.173801 0.359689 -0.167212 -1.76155 -0.0854062 -0.0213202 -0.736739 -0.0371832 -0.152647 julia> M_svd = fit(PCA, x, method=:svd) PCA(indim = 4, outdim = 3, principalratio = 0.9947878161267246) julia> loadings(M_svd) 4×3 Matrix{Float64}: -0.740627 -0.322366 0.162227 0.173221 -0.358488 -0.166653 -1.75566 0.085121 -0.021249 -0.734279 0.037059 -0.152137 julia> n = size(x, 2) 150 julia> loadings(M_svd) .* sqrt(n/(n-1)) 4×3 Matrix{Float64}: -0.743108 -0.323446 0.16277 0.173801 -0.359689 -0.167212 -1.76155 0.0854062 -0.0213202 -0.736739 0.0371832 -0.152647

[wildart]

Ah, I used my dev copy that has no error. The problem actually in the different line:

MultivariateStats.jl/src/pca.jl

Line 219 in 99ee965

@inbounds v[i] = abs2(v[i]) / n

The eigenvalue should be scaled by n-1