Recommender systems

Level UniversityDifficulty ★★★★★Application⌖ Open in the map

What is it?

Predict how much a user will like an item as the dot product of learned vectors, $\hat r_{ui} = p_u\cdot q_i$ , fitted by (stochastic) gradient descent on the known ratings with regularization.

Formulas

\min_{P,Q}\sum_{(u,i)}\big(r_{ui} - p_u\cdot q_i\big)^2 + \lambda\big(\norm{p_u}^2 + \norm{q_i}^2\big)

The mathematics behind it

Dot product★★★★★frequent
Predicted affinity between a user and an item is the dot product of their embedding vectors.

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.