Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fast Disentangled Slim Tensor Learning for Multi-view Clustering

Deng Xu, Chao Zhang, Zechao Li, Chunlin Chen, Huaxiong Li

TL;DR

A new approach termed fast Disentangled Slim Tensor Learning (DSTL) for multi-view clustering, which directly explores the high-order correlations among multi-view latent semantic representations based on matrix factorization and alleviates the negative influence of feature redundancy.

Abstract

Tensor-based multi-view clustering has recently received significant attention due to its exceptional ability to explore cross-view high-order correlations. However, most existing methods still encounter some limitations. (1) Most of them explore the correlations among different affinity matrices, making them unscalable to large-scale data. (2) Although some methods address it by introducing bipartite graphs, they may result in sub-optimal solutions caused by an unstable anchor selection process. (3) They generally ignore the negative impact of latent semantic-unrelated information in each view. To tackle these issues, we propose a new approach termed fast Disentangled Slim Tensor Learning (DSTL) for multi-view clustering . Instead of focusing on the multi-view graph structures, DSTL directly explores the high-order correlations among multi-view latent semantic representations based on matrix factorization. To alleviate the negative influence of feature redundancy, inspired by robust PCA, DSTL disentangles the latent low-dimensional representation into a semantic-unrelated part and a semantic-related part for each view. Subsequently, two slim tensors are constructed with tensor-based regularization. To further enhance the quality of feature disentanglement, the semantic-related representations are aligned across views through a consensus alignment indicator. Our proposed model is computationally efficient and can be solved effectively. Extensive experiments demonstrate the superiority and efficiency of DSTL over state-of-the-art approaches. The code of DSTL is available at https://github.com/dengxu-nju/DSTL.

Fast Disentangled Slim Tensor Learning for Multi-view Clustering

TL;DR

A new approach termed fast Disentangled Slim Tensor Learning (DSTL) for multi-view clustering, which directly explores the high-order correlations among multi-view latent semantic representations based on matrix factorization and alleviates the negative influence of feature redundancy.

Abstract

Tensor-based multi-view clustering has recently received significant attention due to its exceptional ability to explore cross-view high-order correlations. However, most existing methods still encounter some limitations. (1) Most of them explore the correlations among different affinity matrices, making them unscalable to large-scale data. (2) Although some methods address it by introducing bipartite graphs, they may result in sub-optimal solutions caused by an unstable anchor selection process. (3) They generally ignore the negative impact of latent semantic-unrelated information in each view. To tackle these issues, we propose a new approach termed fast Disentangled Slim Tensor Learning (DSTL) for multi-view clustering . Instead of focusing on the multi-view graph structures, DSTL directly explores the high-order correlations among multi-view latent semantic representations based on matrix factorization. To alleviate the negative influence of feature redundancy, inspired by robust PCA, DSTL disentangles the latent low-dimensional representation into a semantic-unrelated part and a semantic-related part for each view. Subsequently, two slim tensors are constructed with tensor-based regularization. To further enhance the quality of feature disentanglement, the semantic-related representations are aligned across views through a consensus alignment indicator. Our proposed model is computationally efficient and can be solved effectively. Extensive experiments demonstrate the superiority and efficiency of DSTL over state-of-the-art approaches. The code of DSTL is available at https://github.com/dengxu-nju/DSTL.

Paper Structure

This paper contains 21 sections, 3 theorems, 34 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notations and Related Work
  3. Notations and Preliminaries
  4. Multi-view Matrix Factorization
  5. Tensor-based Multi-view Clustering
  6. The Proposed Method
  7. Model Formulation
  8. Optimization
  9. Computational Complexity Analysis
  10. Space Complexity
  11. Time Complexity
  12. Convergence Analysis
  13. Experiment
  14. Experimental Setup
  15. Experimental Results
  16. ...and 6 more sections

Key Result

Theorem 1

Let $\mathbf{B}=\mathbf{U}\mathbf{\Sigma}\mathbf{V}^T$ be the singular value decomposition (SVD) of a matrix $\mathbf{B}$. The optimal solution to the problem is given by $\mathbf{B}^\dagger=\mathbf{V}\mathbf{U}^T$.

Figures (6)

  • Figure 1: The overall framework of DSTL.
  • Figure 2: The sensitivity analysis of clustering results of DSTL w.r.t. $\lambda_1$ and $\lambda_2$ on (a) NGs, (b) BBCSport, (c) HW and (d) NUSWIDEOBJ datasets.
  • Figure 3: The sensitivity analysis of clustering results of DSTL w.r.t. $\lambda_3$ and $k$ on (a) NGs, (b) BBCSport, (c) HW and (d) NUSWIDEOBJ datasets.
  • Figure 4: The condition value and ACC w.r.t. the number of iterations on (a) NGs, (b) BBCSport, (c) HW and (d) NUSWIDEOBJ datasets.
  • Figure 5: The t-SNE visualizations of learned consensus alignment indicator obtained by DSTL-S (left) and DSTL (right) on (a) BBCSport, (b) HW, (c) Scene15 and (d) Animal datasets.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Definition 1: t-SVD kilmer2013third
  • Definition 2: t-SVD based tensor nuclear norm semerci2014tensor
  • Theorem 1
  • Theorem 2
  • Theorem 3