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