Hierarchical Alternating Least Squares Methods for Quaternion Nonnegative Matrix Factorizations

TL;DR

This paper introduces a hierarchical nonnegative least squares algorithm for quaternion nonnegative matrix factorization, effectively processing RGB color and polarization images with proven convergence and superior performance over existing methods.

Contribution

The paper presents a novel hierarchical least squares approach for QNMF, including convergence analysis and validation on polarization and facial image datasets.

Findings

Effective in polarization image representation

Improves color facial image analysis

Outperforms state-of-the-art methods

Abstract

In this report, we discuss a simple model for RGB color and polarization images under a unified framework of quaternion nonnegative matrix factorization (QNMF) and present a hierarchical nonnegative least squares method to solve the factor matrices. The convergence analysis of the algorithm is discussed as well. We test the proposed method in the polarization image and color facial image representation. Compared to the state-of-the-art methods, the experimental results demonstrate the effectiveness of the hierarchical nonnegative least squares method for the QNMF model.