Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization

TL;DR

This paper introduces an adaptive graph regularized NMF method that integrates multiple kernel learning to refine the data graph structure, leading to improved clustering performance.

Contribution

It proposes a novel kernel learning approach within the GrNMF framework to enhance the data representation and clustering quality.

Findings

Outperforms state-of-the-art clustering algorithms like NMF, GrNMF, SVD.

Demonstrates improved data representation through kernel-refined graphs.

Shows encouraging results in various datasets.

Abstract

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.