Fair Recommendation by Geometric Interpretation and Analysis of Matrix Factorization
This work addresses fairness issues in recommender systems, which is an incremental improvement over existing methods.
The paper tackles the problem of fairness in matrix factorization-based recommender systems by reformulating angle-preserving dimensionality reduction into distance-preserving dimensionality reduction, showing that ParaMat achieves the highest fairness compared to 8 other algorithms, including ZeroMat and DotMat Hybrid.
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.