# Nonnegative Matrix Factorization with Local Similarity Learning

arXiv: https://arxiv.org/abs/1907.04150 · HTML: https://mlsanity.com/paper/1907.04150/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization](https://mlsanity.com/paper/2201.02812/) (2022)
- [Initialization for Nonnegative Matrix Factorization: a Comprehensive Review](https://mlsanity.com/paper/2109.03874/) (2021)
- [Log-based Sparse Nonnegative Matrix Factorization for Data Representation](https://mlsanity.com/paper/2204.10647/) (2022)

## Abstract (arXiv)

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.