Rethinking Popularity Bias in Collaborative Filtering via Analytical Vector Decomposition

TL;DR

This paper identifies that popularity bias in collaborative filtering arises from the geometric organization of item embeddings due to BPR optimization, and proposes a correction framework that improves personalization and fairness.

Contribution

The paper reveals the intrinsic geometric cause of popularity bias in BPR-based CF models and introduces DDC, a universal correction method that disentangles preference from popularity.

Findings

DDC significantly reduces training loss compared to baselines.

DDC improves recommendation quality and fairness.

Popularity bias is an inherent geometric artifact of BPR optimization.

Abstract

Popularity bias fundamentally undermines the personalization capabilities of collaborative filtering (CF) models, causing them to disproportionately recommend popular items while neglecting users' genuine preferences for niche content. While existing approaches treat this as an external confounding factor, we reveal that popularity bias is an intrinsic geometric artifact of Bayesian Pairwise Ranking (BPR) optimization in CF models. Through rigorous mathematical analysis, we prove that BPR systematically organizes item embeddings along a dominant "popularity direction" where embedding magnitudes directly correlate with interaction frequency. This geometric distortion forces user embeddings to simultaneously handle two conflicting tasks-expressing genuine preference and calibrating against global popularity-trapping them in suboptimal configurations that favor popular items regardless of individual tastes. We propose Directional Decomposition and Correction (DDC), a universally applicable framework that surgically corrects this embedding geometry through asymmetric directional updates. DDC guides positive interactions along personalized preference directions while steering negative interactions away from the global popularity direction, disentangling preference from popularity at the geometric source. Extensive experiments across multiple BPR-based architectures demonstrate that DDC significantly outperforms state-of-the-art debiasing methods, reducing training loss to less than 5% of heavily-tuned baselines while achieving superior recommendation quality and fairness. Code is available in https://github.com/LingFeng-Liu-AI/DDC.