A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering. (October 2018)

• Record Type: Journal Article
• Authors: Tolić, Dijana; Antulov-Fantulin, Nino; Kopriva, Ivica
• Is Part Of: Pattern recognition. Volume 82(2018:Oct.)
• Page Start: 40
• Page End: 55
• Publication Date: 2018-10
• Subjects: Subspace clustering -- Non-negative matrix factorization -- Orthogonality -- Kernels -- Graph regularization; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2018.04.029
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: Subspace clustering is solved from nonlinear orthogonal NMF perspective. General kernel-based multiplicative orthogonal updates for NMF are derived. Explicit orthogonality constraint excludes the usual k-means clustering step. The local geometric structure is included via fully connected graph regularization. A connection between spectral clustering and kernel orthogonal NMF is established. 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.