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One-Step Multi-View Clustering Based on Transition Probability

Wenhui Zhao, Quanxue Gao, Guangfei Li, Cheng Deng, Ming Yang

TL;DR

This work introduces the One-Step Multi-View Clustering Based on Transition Probability (OSMVC-TP), a probabilistic approach, which leverages the anchor graph, representing the transition probabilities from samples to anchor points, and calculates the transition probabilities from samples to categories, enhancing the interpretability of clustering.

Abstract

The large-scale multi-view clustering algorithms, based on the anchor graph, have shown promising performance and efficiency and have been extensively explored in recent years. Despite their successes, current methods lack interpretability in the clustering process and do not sufficiently consider the complementary information across different views. To address these shortcomings, we introduce the One-Step Multi-View Clustering Based on Transition Probability (OSMVC-TP). This method adopts a probabilistic approach, which leverages the anchor graph, representing the transition probabilities from samples to anchor points. Our method directly learns the transition probabilities from anchor points to categories, and calculates the transition probabilities from samples to categories, thus obtaining soft label matrices for samples and anchor points, enhancing the interpretability of clustering. Furthermore, to maintain consistency in labels across different views, we apply a Schatten p-norm constraint on the tensor composed of the soft labels. This approach effectively harnesses the complementary information among the views. Extensive experiments have confirmed the effectiveness and robustness of OSMVC-TP.

One-Step Multi-View Clustering Based on Transition Probability

TL;DR

This work introduces the One-Step Multi-View Clustering Based on Transition Probability (OSMVC-TP), a probabilistic approach, which leverages the anchor graph, representing the transition probabilities from samples to anchor points, and calculates the transition probabilities from samples to categories, enhancing the interpretability of clustering.

Abstract

The large-scale multi-view clustering algorithms, based on the anchor graph, have shown promising performance and efficiency and have been extensively explored in recent years. Despite their successes, current methods lack interpretability in the clustering process and do not sufficiently consider the complementary information across different views. To address these shortcomings, we introduce the One-Step Multi-View Clustering Based on Transition Probability (OSMVC-TP). This method adopts a probabilistic approach, which leverages the anchor graph, representing the transition probabilities from samples to anchor points. Our method directly learns the transition probabilities from anchor points to categories, and calculates the transition probabilities from samples to categories, thus obtaining soft label matrices for samples and anchor points, enhancing the interpretability of clustering. Furthermore, to maintain consistency in labels across different views, we apply a Schatten p-norm constraint on the tensor composed of the soft labels. This approach effectively harnesses the complementary information among the views. Extensive experiments have confirmed the effectiveness and robustness of OSMVC-TP.
Paper Structure (15 sections, 2 theorems, 33 equations, 7 figures, 4 tables, 1 algorithm)

This paper contains 15 sections, 2 theorems, 33 equations, 7 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Probability Transition Process
  3. Methodology
  4. Motivation and Objective Function
  5. Optimization
  6. Experiment
  7. Datasets and Metrics
  8. Compared methods
  9. Experimental results
  10. Ablation study
  11. Effect of parameter p
  12. Effect of lambda
  13. T-SNE results analysis
  14. Convergence analysis
  15. Conclusion

Key Result

Theorem 1

GaoXCDGL19 Given the compact singular value decomposition (SVD) of $\mathbf{W}$ as $\mathbf{U}\mathbf{\Sigma}\mathbf{V}^{\mathrm{T}}$, the optimal solution for is given by $\mathbf{M} = \mathbf{U}\mathbf{V}^{\mathrm{T}}$.

Figures (7)

  • Figure 1: An anchor graph representation of samples and anchors.
  • Figure 2: The anchor graph $\mathbf{S}^{(v)}$ can represent the transition probabilities from samples to anchor points. If the transition probabilities from anchor points to categories $\mathbf{H}^{(v)}$ are known, it is possible to directly compute the transition probabilities from samples to categories. The Schatten p-norm is applied to complementary information.
  • Figure 3: Construction of $\bm{\mathcal{G}} \in \mathbb{R}^{n\times v \times c}$. $\Delta^{(c)}$ is the $c$-th frontal slice of $\bm{\mathcal{G}}$.
  • Figure 4: The clustering performances expressed by t-SNE.
  • Figure 5: Clustering performance vs. $p$ on four datasets.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Definition 1
  • Remark 1
  • Remark 2
  • Theorem 1
  • Theorem 2