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Nonconvex low-rank tensor approximation with graph and consistent regularizations for multi-view subspace learning.

Baicheng Pan1, Chuandong Li1, Hangjun Che1

  • 1Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.

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|February 24, 2023
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Summary
This summary is machine-generated.

This study introduces a novel nonconvex low-rank tensor approximation with graph and consistent regularizations (NLRTGC) model for multi-view subspace learning. NLRTGC enhances clustering by incorporating local graph information and improving tensor rank estimation.

Keywords:
Multi-view clusteringNonconvex low-rank tensor approximationSpectral clusteringSubspace clustering

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Area of Science:

  • Machine Learning
  • Data Science
  • Computer Vision

Background:

  • Multi-view clustering enhances performance by integrating information from multiple data perspectives.
  • Subspace clustering using tensor learning, particularly Markov chain-based methods, is a key area in multi-view clustering.
  • Existing tensor learning methods often neglect local graph information, inter-view relationships, and use biased tensor rank estimations.

Purpose of the Study:

  • To propose a novel model, Nonconvex Low-Rank Tensor Approximation with Graph and Consistent regularizations (NLRTGC), for multi-view subspace learning.
  • To address limitations of current tensor learning methods by incorporating local manifold information and inter-view consistency.
  • To improve the accuracy of tensor rank approximation in multi-view clustering.

Main Methods:

  • Developed the NLRTGC model incorporating graph regularization to preserve local manifold information.
  • Implemented consistent regularization between multiple views to maintain the diagonal block structure of representation matrices.
  • Utilized a nonnegative nonconvex low-rank tensor kernel function and the alternating direction method of multipliers (ADMM) for optimization.

Main Results:

  • The proposed NLRTGC model effectively retains local manifold information and inter-view relationships.
  • The use of a nonconvex low-rank tensor kernel reduces rank estimation deviation compared to traditional methods.
  • Experimental results demonstrate the superiority of NLRTGC over state-of-the-art algorithms on various datasets.

Conclusions:

  • NLRTGC offers a significant advancement in multi-view subspace clustering by addressing key limitations of existing methods.
  • The model's ability to integrate local and global information leads to improved clustering performance.
  • NLRTGC shows strong effectiveness and robustness, particularly on noisy and real-world datasets.