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Nonlinear subspace clustering by functional link neural networks

Long Shi, Lei Cao, Zhongpu Chen, Badong Chen, Yu Zhao

TL;DR

This work tackles nonlinear subspace clustering by adopting a lightweight functional-link neural network (FLNN) to nonlinearly map data and learn a self-representation matrix in the transformed space, achieving favorable clustering with reduced computation. It introduces a grouping (local similarity) regularization and a convex-combination scheme (CCSC) that jointly leverages linear and nonlinear representations via a tunable parameter $\lambda$. The proposed FLNNSC and CCSC demonstrate superior clustering performance and efficiency across multiple benchmarks, with extensive analyses on affinity structure, parameter sensitivity, convergence, and execution time. The methods advance practical nonlinear subspace clustering by balancing accuracy and cost, and the authors outline directions for adaptive parameter schemes and higher-order expansions. Overall, the paper provides a cohesive framework for efficient nonlinear subspace clustering with empirically strong results and clear avenues for future work.

Abstract

Nonlinear subspace clustering based on a feed-forward neural network has been demonstrated to provide better clustering accuracy than some advanced subspace clustering algorithms. While this approach demonstrates impressive outcomes, it involves a balance between effectiveness and computational cost. In this study, we employ a functional link neural network to transform data samples into a nonlinear domain. Subsequently, we acquire a self-representation matrix through a learning mechanism that builds upon the mapped samples. As the functional link neural network is a single-layer neural network, our proposed method achieves high computational efficiency while ensuring desirable clustering performance. By incorporating the local similarity regularization to enhance the grouping effect, our proposed method further improves the quality of the clustering results. Additionally, we introduce a convex combination subspace clustering scheme, which combining a linear subspace clustering method with the functional link neural network subspace clustering approach. This combination approach allows for a dynamic balance between linear and nonlinear representations. Extensive experiments confirm the advancement of our methods. The source code will be released on https://lshi91.github.io/ soon.

Nonlinear subspace clustering by functional link neural networks

TL;DR

This work tackles nonlinear subspace clustering by adopting a lightweight functional-link neural network (FLNN) to nonlinearly map data and learn a self-representation matrix in the transformed space, achieving favorable clustering with reduced computation. It introduces a grouping (local similarity) regularization and a convex-combination scheme (CCSC) that jointly leverages linear and nonlinear representations via a tunable parameter . The proposed FLNNSC and CCSC demonstrate superior clustering performance and efficiency across multiple benchmarks, with extensive analyses on affinity structure, parameter sensitivity, convergence, and execution time. The methods advance practical nonlinear subspace clustering by balancing accuracy and cost, and the authors outline directions for adaptive parameter schemes and higher-order expansions. Overall, the paper provides a cohesive framework for efficient nonlinear subspace clustering with empirically strong results and clear avenues for future work.

Abstract

Nonlinear subspace clustering based on a feed-forward neural network has been demonstrated to provide better clustering accuracy than some advanced subspace clustering algorithms. While this approach demonstrates impressive outcomes, it involves a balance between effectiveness and computational cost. In this study, we employ a functional link neural network to transform data samples into a nonlinear domain. Subsequently, we acquire a self-representation matrix through a learning mechanism that builds upon the mapped samples. As the functional link neural network is a single-layer neural network, our proposed method achieves high computational efficiency while ensuring desirable clustering performance. By incorporating the local similarity regularization to enhance the grouping effect, our proposed method further improves the quality of the clustering results. Additionally, we introduce a convex combination subspace clustering scheme, which combining a linear subspace clustering method with the functional link neural network subspace clustering approach. This combination approach allows for a dynamic balance between linear and nonlinear representations. Extensive experiments confirm the advancement of our methods. The source code will be released on https://lshi91.github.io/ soon.
Paper Structure (19 sections, 25 equations, 7 figures, 7 tables)

This paper contains 19 sections, 25 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Review of SSC and LRR
  4. Fundamentals of FLNN
  5. FLNN subspace clustering
  6. Model formulation
  7. Optimization
  8. Computational complexity analysis
  9. Convex combination subspace clustering
  10. Experiments
  11. Experimental settings
  12. Evaluation of clustering performance
  13. Performance comparison
  14. Affinity graphs analysis
  15. Parameter sensitivity and convergence analysis
  16. ...and 4 more sections

Figures (7)

  • Figure 1: Framework of FLNNSC, where $\mathbf{F.E.}$ in a FLNN represents the functional expansion module.
  • Figure 2: CA, NMI, ARI and F1 score of the proposed CCSC with respect to $\lambda$ on the USPS and COIL20 datasets.
  • Figure 3: Affinity graphs produced by (a) SSC, (b) LRR, (c) LRSC, (d) NSC, (e) SMR, (f) KSSC, (g) LSR1, (h) LSR2, (i) KTRR, (j) BDR-B, (k) BDR-Z, (l) FLNNSC on the USPS.
  • Figure 4: CA, NMI, ARI and F1 score with different $\alpha$ and $\beta$ combinations on the Extended Yale B (10 subjects), USPS and COIL20 datasets.
  • Figure 5: Convergence analysis on the Extended Yale B, USPS and COIL20 datasets.
  • ...and 2 more figures