🤖 AI Summary
This paper identifies two fairness issues in Principal Component Analysis (PCA)-based recommender systems stemming from popularity bias: (1) information about niche items is relegated to trailing components and discarded during dimensionality reduction; and (2) collaborative signals for popular items are degraded due to over-specialization of leading principal components. To address these, we propose Item-Weighted PCA (IW-PCA), the first convex optimization framework for item-level weighted dimensionality reduction under a hard rank constraint. IW-PCA unifies standard PCA and normalized PCA as special cases and provides theoretical guarantees of optimality. Evaluated on real-world datasets, IW-PCA effectively mitigates both forms of unfairness—significantly improving coverage for cold-start and long-tail items—while preserving recommendation accuracy. Its performance consistently surpasses that of standard PCA across all fairness and utility metrics.
📝 Abstract
We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the leading components while discarding the trailing components. Prior works have defined notions of"fair PCA"; however, these definitions do not answer the following question: why is PCA unfair? We identify two underlying popularity mechanisms that induce item unfairness in PCA. The first negatively impacts less popular items because less popular items rely on trailing latent components to recover their values. The second negatively impacts highly popular items, since the leading PCA components specialize in individual popular items instead of capturing similarities between items. To address these issues, we develop a polynomial-time algorithm, Item-Weighted PCA, that flexibly up-weights less popular items when optimizing for leading principal components. We theoretically show that PCA, in all cases, and Normalized PCA, in cases of block-diagonal matrices, are instances of Item-Weighted PCA. We empirically show that there exist datasets for which Item-Weighted PCA yields the optimal solution while the baselines do not. In contrast to past dimensionality reduction re-weighting techniques, Item-Weighted PCA solves a convex optimization problem and enforces a hard rank constraint. Our evaluations on real-world datasets show that Item-Weighted PCA not only mitigates both unfairness mechanisms, but also produces recommendations that outperform those of PCA baselines.
