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Clustering Result Re-guided Incomplete Multi-view Spectral Clustering

Jun Yin, Runcheng Cai, Shiliang Sun

TL;DR

This work tackles incomplete multi-view clustering, where missing views complicate joint representation learning and clustering. CRG_IMSC integrates clustering into the learning objective by enforcing a nonnegative common representation $U$, constructing a connectivity matrix through $U^T U$, and guiding spectral learning with a self-representation residual based on this connectivity. The method optimizes via alternating updates: eigen-decomposition to update per-view representations $U^{v}$ and a multiplicative-update rule to refine the shared $U$, with a rigorous convergence proof. Empirically, CRG_IMSC outperforms state-of-the-art baselines across several missing-view settings on four public datasets, demonstrating robustness to incomplete data and the benefits of clustering-result guidance in multi-view clustering.

Abstract

Incomplete multi-view spectral clustering generalizes spectral clustering to multi-view data and simultaneously realizes the partition of multi-view data with missing views. For this category of method, K-means algorithm needs to be performed to generate the clustering result after the procedure of feature extraction. More importantly, the connectivity of samples reflected by the clustering result is not utilized effectively. To overcome these defects, we propose Clustering Result re-Guided Incomplete Multi-view Spectral Clustering (CRG_IMSC). CRG_IMSC obtains the clustering result directly by imposing nonnegative constraint to the extracted feature. Furthermore, it constructs the connectivity matrix according to the result of spectral clustering, and minimizes the residual of self-representation based on the connectivity matrix. A novel iterative algorithm using multiplicative update is developed to solve the optimization problem of CRG_IMSC, and its convergence is proved rigorously. On benchmark datasets, for multi-view data, CRG_IMSC performs better than state-of-the-art clustering methods, and the experimental results also demonstrate the convergence of CRG_IMSC algorithm.

Clustering Result Re-guided Incomplete Multi-view Spectral Clustering

TL;DR

This work tackles incomplete multi-view clustering, where missing views complicate joint representation learning and clustering. CRG_IMSC integrates clustering into the learning objective by enforcing a nonnegative common representation , constructing a connectivity matrix through , and guiding spectral learning with a self-representation residual based on this connectivity. The method optimizes via alternating updates: eigen-decomposition to update per-view representations and a multiplicative-update rule to refine the shared , with a rigorous convergence proof. Empirically, CRG_IMSC outperforms state-of-the-art baselines across several missing-view settings on four public datasets, demonstrating robustness to incomplete data and the benefits of clustering-result guidance in multi-view clustering.

Abstract

Incomplete multi-view spectral clustering generalizes spectral clustering to multi-view data and simultaneously realizes the partition of multi-view data with missing views. For this category of method, K-means algorithm needs to be performed to generate the clustering result after the procedure of feature extraction. More importantly, the connectivity of samples reflected by the clustering result is not utilized effectively. To overcome these defects, we propose Clustering Result re-Guided Incomplete Multi-view Spectral Clustering (CRG_IMSC). CRG_IMSC obtains the clustering result directly by imposing nonnegative constraint to the extracted feature. Furthermore, it constructs the connectivity matrix according to the result of spectral clustering, and minimizes the residual of self-representation based on the connectivity matrix. A novel iterative algorithm using multiplicative update is developed to solve the optimization problem of CRG_IMSC, and its convergence is proved rigorously. On benchmark datasets, for multi-view data, CRG_IMSC performs better than state-of-the-art clustering methods, and the experimental results also demonstrate the convergence of CRG_IMSC algorithm.

Paper Structure

This paper contains 14 sections, 4 theorems, 29 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Multi-view spectral clustering
  4. Incomplete multi-view spectral clustering
  5. Proposed Method
  6. Objective Function
  7. Optimization
  8. Convergence Analysis
  9. Complexity Analysis
  10. Relation to other multi-view clustering methods
  11. Experiments
  12. Datasets
  13. Compared Methods
  14. Experimental Results and Analysis

Key Result

Lemma 1

is an auxiliary function of the objective $L(U)$ in Eq. ref8, where $\hat{Q}^{v}={M^{v}}^T\hat{U}^T\hat{U}M^{v}$.

Figures (2)

  • Figure 1: The framework of CRG_IMSC: In the left side, spectral clustering is performed on the incomplete multi-view data to obtain the clustering result $U$. Then the connectivity matrix which reflects the relationship of different samples can be calculated by $U^TU$. In the right side, based on the connectivity matrix, self-representation is performed to re-guide the incomplete multi-view spectral clustering.
  • Figure 2: NMI of CRG_IMSC versus parameters $\alpha$ and $\beta$ on 3Sources and BBCSport datasets

Theorems & Definitions (4)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1