# Spherical Matrix Factorization

arXiv: https://arxiv.org/abs/2111.14536 · HTML: https://mlsanity.com/paper/2111.14536/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 3 of 3)

- [On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient](https://mlsanity.com/paper/1803.06573/) (2018)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Spherical Principal Component Analysis](https://mlsanity.com/paper/1903.06877/) (2019)

## Built on by (most cited first, 1 of 1)

- [Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective](https://mlsanity.com/paper/2209.02528/) (2022)

## Abstract (arXiv)

Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean and angle distance. However, due to non-convexity of the objective and constraints, the optimized solution is not easy to obtain. In this paper we propose a general framework to systematically solve it with provable convergence guarantee with various constraints.