Spherical Matrix Factorization

TL;DR

This paper introduces a novel matrix factorization framework that unifies Euclidean and angle distance measures, providing a systematic solution with convergence guarantees for non-convex problems.

Contribution

It proposes a general framework for spherical matrix factorization that incorporates both distance measures and offers provable convergence despite non-convexity.

Findings

Framework unifies Euclidean and angle distance in matrix factorization

Provides convergence guarantees for the proposed method

Applicable to various constraints in matrix factorization

Abstract

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.