Collaborative filtering

1 · What it is

Collaborative filtering predicts what one person will like from what other people did. All it needs is a record of past behaviour, like purchases or star ratings. That behaviour goes into a grid called the feedback matrix, with a row for each user and a column for each item. Feedback is explicit when people give a numerical rating. It is implicit when the system infers interest from behaviour, such as someone watching a film. The MovieLens benchmark from GroupLens Research holds 32 million ratings of 87,585 movies by 200,948 users. Even so, most people never rate most films, so nearly all cells stay empty. Content-based filtering is the opposite, matching item traits to what one user already liked.

The earliest methods look for neighbours. User-based methods fill a blank by looking at how people with similar taste scored that item. Item-based methods instead look at how you yourself scored items that resemble it. At Amazon, two products count as related when shoppers who buy the first are unusually likely to pick up the second. Simply counting co-purchases would push a few bestsellers, such as trash bags, to the top for everyone. Item-based picks are also easier to justify to the person getting them.

Matrix factorisation takes a different route and gives every user and every item a short vector of numbers. A predicted rating is the inner product, or dot product, of the user’s vector and the item’s vector. These vectors are embeddings on one shared map, where a user lands near the items they tend to like. Nobody labels the numbers by hand, because training learns them from the matrix. For star ratings, a common recipe fits only the cells that have ratings and adds a regularisation penalty so the model does not overfit. Two common ways to fit the vectors are stochastic gradient descent and weighted alternating least squares. Alternating least squares starts from random vectors, fixes the user vectors while solving for the item vectors, then swaps. Apache Spark’s MLlib library learns these latent factors with alternating least squares. By default it uses 10 latent factors.

Clicks, views and purchases say a lot about what someone likes but little about what they dislike. One answer came from researchers building a recommender for TV shows. Their paper read each observation as a like-or-not signal paired with its own confidence level, not as a rating. It also fitted every user and item pair, not only the observed ones. Spark uses that approach when its implicit feedback option is switched on.