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

Autor: Ivica Kopriva, Nino Antulov-Fantulin, Dijana Tolić
Rok vydání: 2017
Předmět:
Normalization (statistics)
FOS: Computer and information sciences
Computer Science - Machine Learning
Computer science
Machine Learning (stat.ML)
02 engineering and technology
Non-negative matrix factorization
Matrix decomposition
Machine Learning (cs.LG)
Kernel (linear algebra)
Factorization
Artificial Intelligence
Statistics - Machine Learning
0202 electrical engineering
electronic engineering
information engineering
Cluster analysis
Computing
020206 networking & telecommunications
Incomplete LU factorization
Spectral clustering
Manifold
subspace clustering
non-negative matrix factorization
orthogonality
kernels
graph regularization
Nonlinear system
Signal Processing
020201 artificial intelligence & image processing
Computer Vision and Pattern Recognition
Algorithm
TECHNICAL SCIENCES
Software
Zdroj: Pattern Recognition
DOI: 10.48550/arxiv.1709.10323
Popis: 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.
Databáze: OpenAIRE
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