Sponsor
This work is partially supported by NSF Research Training Group Grant DMS-2136228.
Published In
Numerical Linear Algebra with Applications
Document Type
Pre-Print
Publication Date
10-21-2024
Subjects
Multivariate data analysis
Abstract
Non-negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi-Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts-based data representations to include mixed-sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF-related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new L2,1 SNF algorithm that utilizes the noise-insensitive L2,1 norm. We provide monotonic convergence analysis of the L2,1 SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed-sign datasets as well as several randomized mixed-sign matrices to demonstrate the performance superiority of L2,1 SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels.
Rights
© Copyright the author(s) 2024
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DOI
10.1002/nla.2598
Persistent Identifier
https://archives.pdx.edu/ds/psu/42666
Citation Details
Published as: Rhodes, A., Jiang, B., & Jiang, J. (2024). Graph Regularized Sparse L2,1 Semi‐Nonnegative Matrix Factorization for Data Reduction. Numerical Linear Algebra with Applications. Portico.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Graph Regularized Sparse L2,1 Semi‐Nonnegative Matrix Factorization for Data Reduction. Numerical Linear Algebra with Applications.