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

Tolić, Dijana; Antunov-Fantulin, Nino; Kopriva, Ivica (2018) A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering. Pattern Recognition, 82 (10). pp. 40-55. ISSN 0031-3203

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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 nonnegative 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.

Item Type: Article
Additional Information: The authors would like to thank to Mario Lucic and Maria Brbic for proofreading the article. The work of DT is funded by the by the Croatian Science Foundation with the project No. 1-1701-2014 "Machine learning algorithms for insightful analysis of complex data structures". The work of IK is funded by Croatian science foundation with the project IP-2016-06-5235 "Structured Decompositions of Empirical Data for Computationally-Assisted Diagnoses of Disease" and was in part supported by European Regional Development Fund under the grant KK.01.1.1.01.0009 (DATACROSS). The work of NAF is funded by the EU Horizon 2020 SoBigData project under grant agreement No. 654024.
Uncontrolled Keywords: subspace clustering; non-negative matrix factorization; orthogonality; kernels; graph regularization
Subjects: TECHNICAL SCIENCES
TECHNICAL SCIENCES > Computing
TECHNICAL SCIENCES > Computing > Artificial Intelligence
Divisions: Division of Electronics
Projects:
Project titleProject leaderProject codeProject type
Postupci strojnog učenja za dubinsku analizu složenih struktura podataka-Descriptive InductionDragan GambergerIP-2013-11-9623HRZZ
Strukturne dekompozicije empirijskih podataka za računalno potpomognutu dijagnostiku bolesti-DEDADIvica KoprivaIP-2016-06-5235HRZZ
Depositing User: Ivica Kopriva
Date Deposited: 26 Nov 2019 09:05
Last Modified: 01 Oct 2020 23:15
URI: http://fulir.irb.hr/id/eprint/5148
DOI: 10.1016/j.patcog.2018.04.029

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