Linear Structure Analysis of Embeddings for Bias Disparity Reduction in Collaborative Filtering

Recommender systems personalize user experiences by filtering large volumes of information, and further shape user behavior. Collaborative filtering (CF), a widely used algorithm in this domain, learns user preferences from user-item interactions. However, recent studies indicate that certain CF algorithms can excessively amplify inherent data biases, manifesting as bias disparity. In this study, we examine the latent factor model (LFM), a state-of-the-art CF method that represents users and items as vectors in a shared latent space. By applying linear dimensionality reduction techniques with strong interpretability (such as principal component analysis) to LFM embeddings trained on real-world data, we identify specific axes that encode biases. We then demonstrate the application of these linear relationships in mitigating bias disparity. Experimental results show that our proposed approach can reduce bias disparity with only a slight decrease in recommendation accuracy-an average of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5-8\%$</tex-math></inline-formula> with principal component analysis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1-3\%$</tex-math></inline-formula> with independent component analysis.