Nonnegative Matrix Factorization with Local Similarity Learning

TL;DR

This paper introduces a novel nonnegative matrix factorization approach that emphasizes learning local similarities and clustering, resulting in more representative data representations that capture inherent geometric structures.

Contribution

It proposes a new NMF method that jointly learns local similarities and clustering, enhancing data representation by capturing local geometric properties.

Findings

The proposed method effectively captures local data structures.

Experimental results demonstrate improved representation quality.

The algorithm converges efficiently with theoretical guarantees.

Abstract

Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new type of nonnegative matrix factorization method, which learns local similarity and clustering in a mutually enhancing way. The learned new representation is more representative in that it better reveals inherent geometric property of the data. Nonlinear expansion is given and efficient multiplicative updates are developed with theoretical convergence guarantees. Extensive experimental results have confirmed the effectiveness of the proposed model.