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Label Learning Method Based on Tensor Projection

Jing Li, Quanxue Gao, Qianqian Wang, Cheng Deng, Deyan Xie

TL;DR

This work tackles scalable multi-view clustering by bypassing post-processing and bipartite graph learning through a tensor-projection approach that maps anchor graphs directly to clustering labels. By extending projection from a 2D view to a 3D tensor and incorporating a tensor Schatten $p$-norm regularization, the method encourages cross-view consensus while preserving useful complementary information. The proposed optimization uses an augmented Lagrangian framework with efficient G, H, Q, and J updates, yielding convergence in practice. Experiments across several large multi-view datasets demonstrate state-of-the-art performance in ACC, NMI, and Purity, highlighting the method's potential for scalable, high-quality clustering without heavy parameter tuning.

Abstract

Multi-view clustering method based on anchor graph has been widely concerned due to its high efficiency and effectiveness. In order to avoid post-processing, most of the existing anchor graph-based methods learn bipartite graphs with connected components. However, such methods have high requirements on parameters, and in some cases it may not be possible to obtain bipartite graphs with clear connected components. To end this, we propose a label learning method based on tensor projection (LLMTP). Specifically, we project anchor graph into the label space through an orthogonal projection matrix to obtain cluster labels directly. Considering that the spatial structure information of multi-view data may be ignored to a certain extent when projected in different views separately, we extend the matrix projection transformation to tensor projection, so that the spatial structure information between views can be fully utilized. In addition, we introduce the tensor Schatten $p$-norm regularization to make the clustering label matrices of different views as consistent as possible. Extensive experiments have proved the effectiveness of the proposed method.

Label Learning Method Based on Tensor Projection

TL;DR

This work tackles scalable multi-view clustering by bypassing post-processing and bipartite graph learning through a tensor-projection approach that maps anchor graphs directly to clustering labels. By extending projection from a 2D view to a 3D tensor and incorporating a tensor Schatten -norm regularization, the method encourages cross-view consensus while preserving useful complementary information. The proposed optimization uses an augmented Lagrangian framework with efficient G, H, Q, and J updates, yielding convergence in practice. Experiments across several large multi-view datasets demonstrate state-of-the-art performance in ACC, NMI, and Purity, highlighting the method's potential for scalable, high-quality clustering without heavy parameter tuning.

Abstract

Multi-view clustering method based on anchor graph has been widely concerned due to its high efficiency and effectiveness. In order to avoid post-processing, most of the existing anchor graph-based methods learn bipartite graphs with connected components. However, such methods have high requirements on parameters, and in some cases it may not be possible to obtain bipartite graphs with clear connected components. To end this, we propose a label learning method based on tensor projection (LLMTP). Specifically, we project anchor graph into the label space through an orthogonal projection matrix to obtain cluster labels directly. Considering that the spatial structure information of multi-view data may be ignored to a certain extent when projected in different views separately, we extend the matrix projection transformation to tensor projection, so that the spatial structure information between views can be fully utilized. In addition, we introduce the tensor Schatten -norm regularization to make the clustering label matrices of different views as consistent as possible. Extensive experiments have proved the effectiveness of the proposed method.
Paper Structure (14 sections, 3 theorems, 27 equations, 8 figures, 3 tables, 1 algorithm)

This paper contains 14 sections, 3 theorems, 27 equations, 8 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Anchor Graph-Based Multi-View Clustering Methods
  4. Multi-View Clustering Method Based on Projection
  5. Notations
  6. Methodology
  7. Motivation and Objective Function
  8. Optimization
  9. Experiments
  10. Clustering Performance
  11. Parameter Analysis
  12. Experiments of Convergence
  13. Visualization of Experimental Results
  14. Conclusions

Key Result

Theorem 1

Xu2020low For the model: $\mathbf G$ is solved iteratively and $\mathbf G^\ast=\mathbf U \mathbf V^{\mathrm{T}}$, where $\mathbf U$, $\mathbf V$ is from the SVD decomposition: $\mathbf U \mathbf X \mathbf V^{\mathrm{T}} = \mathbf B \mathbf G + \mathbf K$.

Figures (8)

  • Figure 1: Anchor graph space to label space
  • Figure 2: Tensor construction
  • Figure 3: Clustering performance with different anchor rate on MSRC and Mnist4
  • Figure 4: Running time (sec.) with different anchor rate on MSRC and Mnist4
  • Figure 5: Clustering performance with different $p$ on MSRC and Mnist4
  • ...and 3 more figures

Theorems & Definitions (7)

  • Definition 1: t-product kilmer2011factorization
  • Definition 2
  • Remark 1: Explanation of the tensor Schatten $p$-norm
  • Theorem 1
  • Theorem 2
  • Proof 1
  • Lemma 1