
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.
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Taxonomy
TopicsImage Retrieval and Classification Techniques · Face and Expression Recognition · Advanced Image and Video Retrieval Techniques
