Fair Recommendation by Geometric Interpretation and Analysis of Matrix Factorization

TL;DR

This paper introduces ParaMat, a geometric approach to matrix factorization for recommender systems, emphasizing fairness by analyzing data distribution and reformulating the problem into a distance-preserving framework.

Contribution

The paper proposes a novel paraboloid-based matrix factorization method that improves fairness in recommendations by leveraging geometric data analysis.

Findings

ParaMat outperforms 8 existing algorithms in fairness.

Data in recommender systems lies on co-centric circles in high-dimensional space.

ParaMat is more fair compared to ZeroMat and DotMat Hybrid.

Abstract

Matrix factorization-based recommender system is in effect an angle preserving dimensionality reduction technique. Since the frequency of items follows power-law distribution, most vectors in the original dimension of user feature vectors and item feature vectors lie on the same hyperplane. However, it is very difficult to reconstruct the embeddings in the original dimension analytically, so we reformulate the original angle preserving dimensionality reduction problem into a distance preserving dimensionality reduction problem. We show that the geometric shape of input data of recommender system in its original higher dimension are distributed on co-centric circles with interesting properties, and design a paraboloid-based matrix factorization named ParaMat to solve the recommendation problem. In the experiment section, we compare our algorithm with 8 other algorithms and prove our new method is the most fair algorithm compared with modern day recommender systems such as ZeroMat and DotMat Hybrid.