A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering

TL;DR

This paper introduces a nonlinear orthogonal NMF framework with kernel and graph regularization for improved subspace clustering, capturing nonlinear data structures and local geometry.

Contribution

It develops a novel nonlinear orthogonal NMF method with kernel and graph regularization, connecting it to spectral clustering and enhancing clustering accuracy.

Findings

Outperforms state-of-the-art methods in experiments

Effectively captures nonlinear manifold structures

Provides new algorithms KNSC-Ncut and KNSC-Rcut

Abstract

A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernel-based orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlinear orthogonal NMF framework, we propose two subspace clustering algorithms, named kernel-based non-negative subspace clustering KNSC-Ncut and KNSC-Rcut and establish their connection with spectral normalized cut and ratio cut clustering. We further extend the nonlinear orthogonal NMF framework and introduce a graph regularization to obtain a factorization that respects a local geometric structure of the data after the nonlinear mapping. The proposed NMF-based approach to subspace clustering takes into account the nonlinear nature of the manifold, as well as its intrinsic local geometry, which considerably improves the clustering performance when compared to the several recently proposed state-of-the-art methods.