An Intuitive Explanation of Field Aware Factorization Machines

From LM to Poly2 to MF to FM to FFM

In the context of recommender systems, Field Aware Factorization Machines (FFM) are particularly useful because they are able to handle large, sparse datasets with many categorical features.

To understand how FFM came about, let’s nail down some basics and understand why FFM are good and what they’re good for.

Adapted by Author (original photo at bottom of article)

Linear Regression

The simplest model we can think of when we try to model the relationship between a dependent variable and one or more independent variables is a linear regression model.

For example, to predict what ratings a user might give a particular movie, we could use many different features as predictors. However, for simplicity’s sake, let’s assume two variables — the gender (x1) and the genre of the movie (x2).

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In this case, we would end up with the following equation (assume no bias and assume some encoding being done to categorical variables):

We would then solve for the weights w1 and w2. Naturally, the linear regression wouldn’t…