# Singular values for a latent-factor model

Suppose we build a latent-factor model using alternating least squares (ALS) or stochastic gradient descent (SGD). Can we calculate weights for each latent factor, in a similar way to how the singular-value decomposition provides singular values, which tell us how influential each eigenrow/eigencolumn is in the row space/column space? Or, at the very least, is there a way to order the latent factors by influence?

• After posting this question, I thought of a potential approach: After building the model, one could look at the empirical distribution of each of the latent factors among the user- and item-vectors (potentially separately), where by user-/item-vectors I mean the representation of each user/item in the latent-factor space. A toy example: If there are 3 latent factors and the user-vectors are (1, 2, 0), (-1, 2, 1) and (0, 0, 1), then the distributions of the first, second and third latent factors are {-1, 0, 1}, {0, 2, 2} and {0, 1, 1} respectively. Similarly for the item-vectors. – dwolfeu Apr 26 '19 at 10:21