L21RSVD: Robust L21 Norm SVD-Type Latent Factor Models for Rating Prediction

Recommender systems face fundamental challenges, including extreme data sparsity and noisy rating observations. We propose L21RSVD, a robust latent factor model that employs L21 norm regularization within a Singular Value Decomposition framework to mitigate the impact of outliers while preserving low-rank structure. Unlike conventional L2-regularized approaches, our formulation induces group sparsity in the latent factor space, yielding more discriminative user and item representations. We derive three optimization variants: standard L21RSVD, L21RSVD without the squared term, and coefficient-free adaptive L21RSVD. Building upon these, we introduce a fusion strategy that adaptively aggregates predictions based on local data density. Extensive experiments on benchmark datasets demonstrate that L21RSVD substantially outperforms classical collaborative filtering and the SVD-type model. The proposed fusion model achieves state-of-the-art performance, reducing RMSE by up to 31.21% and MAE by up to 42.99% relative to baseline methods.