A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering
By Dijana Tolic, Nino Antulov-Fantulin, Ivica Kopriva. 2017
68 citations recorded by the source corpus.
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.
Subfields: Computer Vision and Pattern Recognition, Urban Studies
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In Computer Vision and Pattern Recognition
- K. J. Joseph
- Vineeth Nallure Balasubramanian
- Piyush Rai
- Soma Biswas
- Sujoy Paul
- Gaurav Aggarwal
- Kai Han
- Arjun Ashok
In Urban Studies
Citations in the corpus
- Novel Class Discovery without Forgetting (2022, methodology): “Following the practice in Clustering and NCD approaches [19,16,35,49], we use clustering accuracy to measure the performance of class discovery on unlabeled data.”