# Fair Recommendation by Geometric Interpretation and Analysis of Matrix Factorization

arXiv: https://arxiv.org/abs/2301.03791 · HTML: https://mlsanity.com/paper/2301.03791/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 14 references that are in the map.
- First posted on arXiv 10 Jan 2023.

## Builds on (most cited first, 9 of 9)

- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [Controlling Fairness and Bias in Dynamic Learning-to-Rank](https://mlsanity.com/paper/2005.14713/) (2020)
- [Modeling Dynamic Attributes for Next Basket Recommendation](https://mlsanity.com/paper/2109.11654/) (2021)
- [MatRec: Matrix Factorization for Highly Skewed Dataset](https://mlsanity.com/paper/2011.04395/) (2020)
- [Zipf Matrix Factorization : Matrix Factorization with Matthew Effect Reduction](https://mlsanity.com/paper/2106.07347/) (2021)
- [ZeroMat: Solving Cold-start Problem of Recommender System with No Input Data](https://mlsanity.com/paper/2112.03084/) (2021)
- [KL-Mat : Fair Recommender System via Information Geometry](https://mlsanity.com/paper/2204.13583/) (2022)
- [DotMat: Solving Cold-start Problem and Alleviating Sparsity Problem for Recommender Systems](https://mlsanity.com/paper/2206.00151/) (2022)
- [PoissonMat: Remodeling Matrix Factorization using Poisson Distribution and Solving the Cold Start Problem without Input Data](https://mlsanity.com/paper/2212.10460/) (2022)

## Abstract (arXiv)

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.