On Tue, Jun 14, 2011 at 3:35 PM, Dmitriy Lyubimov <[email protected]> wrote: > > Normalization means that second norm of columns in the eigenvector > matrix (i.e. all columns) is 1. In classic SVD A=U*Sigma*V', even if > it is a thin one, U and V are orthonormal. I might be wrong but i was > under impression that i saw some discussion saying Lanczos singular > vector matrix is not necessarily orthonormal (although columns do form > orthogonal basis). I might be wrong about it. >
LanczosSolver normalizes the singular vectors (LanczosSolver.java, line 162), and yes, returns V, not U: if U is documents x latent factors (so gives the projection of each input document onto the reduced basis), and V is latent factors x terms (and has rows which gives each show which latent factors are made up of what terms). Lanczos solver doesn't keep track of documents (partly for scalability: documents can be thought of as "training" your latent factor model), but they instead return the latent factor by term "model": V. -jake
