User Factor

A recommender that was never told what a genre is still ends up holding a compact numerical summary of your taste. The user factor is that summary: a short vector, typically thirty-two to a few hundred numbers, living in the same space as every item in the catalogue.

How the vector is learned
Nobody defines the dimensions. Factorisation fits a vector for every user and every item so that their dot product reproduces the interactions actually observed — stochastic gradient descent over known ratings in the Funk SVD line, alternating least squares over confidence-weighted implicit counts in implicit ALS — both regularised, so a user with six interactions does not acquire an extreme vector. Individual coordinates mean nothing on their own. The geometry carries the information: users who liked the same handful of obscure films end up close together.

What it gives you

• Scoring is a dot product, so a single matrix multiply ranks the whole catalogue for one user.
• It is the same object as a user embedding — the vector a user tower emits in a two-tower retrieval model plays exactly this role, which is why matrix factorisation reads as the simplest neural recommender.
• One short vector stands in for an entire history at serving time, which is what makes nearest-neighbour retrieval over millions of items affordable.

The limits
A user with no interactions has no factor at all, because nothing was ever fitted for them — the hard edge of new-user cold start, and the reason a fresh account gets popularity or content-based suggestions. The vector is also only as current as the last training run, so last night's viewing stays invisible until the model is refitted or the user is folded in.