A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering
This work addresses subspace clustering for data analysis by proposing an incremental method that incorporates nonlinearity and local geometry into NMF.
The authors tackled subspace clustering by introducing a nonlinear orthogonal non-negative matrix factorization (NMF) framework with kernel-based algorithms, which improved clustering performance compared to recent state-of-the-art methods.
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.