Matrix Factorization (d2l.ai)

Abstraction: Collaborative filtering via low-rank user-item interaction matrix decomposition

Key points:

• Matrix factorization decomposes the m×n user-item rating matrix R into user latent matrix P (m×k) and item latent matrix Q (n×k) where k << m,n; predicted rating is dot product of user and item latent vectors plus bias terms
• First proposed by Simon Funk in a 2006 blog post; became prominent through the Netflix Prize ($1M, won by BellKor's Pragmatic Chaos team), where MF played a critical role
• Objective: minimize MSE over known ratings with L2 regularization on P, Q, and bias terms; optimized with SGD or Adam
• User and item biases are added to account for systematic rating tendencies (generous raters, low-quality items)
• Implemented in d2l.ai using nn.Embedding for latent factors; latent dim 30 achieves test RMSE ~1.066 on MovieLens-100K
• RMSE is the standard evaluation metric for rating prediction tasks

Connections: D2l AI · Matrix Factorization · Collaborative Filtering · Recommender Systems

Source: https://d2l.ai/chapter_recommender-systems/mf.html