Latent Geometry of Taste: Scalable Low-Rank Matrix Factorization for Recommender Systems

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