Latent Geometry of Taste: Scalable Low-Rank Matrix Factorization
Joshua Salako
TL;DR
The paper tackles scalable collaborative filtering under extreme sparsity by learning low-rank latent factors via a highly optimized Alternating Least Squares framework on the MovieLens 32M dataset. It compares a bias-only model to a bias-plus-trait-vector MF, showing that a constrained low-rank model (best at $k=10$, $\lambda=0.1$, $\tau=0.25$) generalizes well, with the latent space revealing semantic genre clusters without supervision. Latent embeddings are visualized after PCA, confirming that interaction data alone encodes meaningful structure, and the model supports practical cold-start scoring with a tunable mix of popularity and personalization via $\alpha$. The approach demonstrates scalable, interpretable recommendations and provides a practical deployment path (e.g., a Streamlit app) for real-world systems.
Abstract
Scalability and data sparsity remain critical bottlenecks for collaborative filtering on massive interaction datasets. This work investigates the latent geometry of user preferences using the MovieLens 32M dataset, implementing a high-performance, parallelized Alternating Least Squares (ALS) framework. Through extensive hyperparameter optimization, we demonstrate that constrained low-rank models significantly outperform higher dimensional counterparts in generalization, achieving an optimal balance between Root Mean Square Error (RMSE) and ranking precision. We visualize the learned embedding space to reveal the unsupervised emergence of semantic genre clusters, confirming that the model captures deep structural relationships solely from interaction data. Finally, we validate the system's practical utility in a cold-start scenario, introducing a tunable scoring parameter to manage the trade-off between popularity bias and personalized affinity effectively. The codebase for this research can be found here: https://github.com/joshsalako/recommender.git