Implicit MF
Nobody rates most of what they watch, play or buy. What a recommender actually holds is a log of things that happened — a track played, a product bought — with no record anywhere of what was disliked. Implicit MF is matrix factorization rebuilt around that asymmetry.
Every blank cell counts, but softly
Explicit factorization fits only the cells a user filled in. Implicit MF fits the whole matrix: an observed interaction becomes a target of 1, every unobserved pair a 0, and each cell carries a confidence weight that grows with the strength of the signal — classically 1 + α times the play count. Three hundred plays and one play both mean "liked", but the model is allowed to believe the first far more.
Why it is solved with ALS
Touching every user-item pair would be hopeless with stochastic gradient descent over billions of zeros. Alternating Least Squares sidesteps the problem: with the item factors held fixed, each user's factors have a closed-form solution whose costly part depends only on the full item matrix, which is computed once per iteration and reused. That is why implicit ALS trains on a full catalogue on a single machine — the implicit library does exactly this on Last.fm play counts.
What it hands the pipeline
The output is a factor vector per user and per item, which is precisely what a retrieval stage needs to pull candidates by nearest-neighbour search. Its weakness is inherited from its input: heavily consumed items get strong factors, so popularity bias arrives built in, and a brand-new item has nothing to factorize at all.
Implicit MF is matrix factorization adapted to interaction data that carries no explicit ratings. Observed interactions are treated as positive preference and every unobserved user-item pair as a weak negative, each cell weighted by a confidence that grows with the strength of the signal. Fitting the full matrix rather than the observed entries alone is what stops the model scoring everything highly, and Alternating Least Squares makes that full objective tractable at catalogue scale.
Most of us never rate anything. We just watch, listen and buy — and a recommender has to work out our taste from that alone.
Implicit MF is the method that learns from those actions. It assumes that what you did engage with, you probably liked, and that everything you never touched you probably would not have chosen — but only probably, because you may simply never have seen it. The more often you did something, the more the system trusts that signal. From all of this it builds a short summary of your taste and a matching summary of every item, then puts the two side by side.