Fair recommendation by geometric interpretation and analysis of matrix factorization

Hao Wang

doi:10.1117/12.2659086

23 November 2022 Fair recommendation by geometric interpretation and analysis of matrix factorization

Hao Wang

Proceedings Volume 12454, International Symposium on Robotics, Artificial Intelligence, and Information Engineering (RAIIE 2022); 124540W (2022) https://doi.org/10.1117/12.2659086
Event: International Symposium on Robotics, Artificial Intelligence, and Information Engineering (RAIIE 2022), 2022, Hohhot, China

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.

Citation Download Citation

Hao Wang "Fair recommendation by geometric interpretation and analysis of matrix factorization", Proc. SPIE 12454, International Symposium on Robotics, Artificial Intelligence, and Information Engineering (RAIIE 2022), 124540W (23 November 2022); https://doi.org/10.1117/12.2659086

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