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Hypergraph regularized nonnegative triple decomposition for multiway data analysis.

Qingshui Liao1,2, Qilong Liu3, Fatimah Abdul Razak4

  • 1Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia. Liaoqingshui2021@163.com.

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This study introduces a novel hypergraph regularized nonnegative triple decomposition for multiway data analysis. This method effectively models complex data relationships, outperforming existing techniques in real-world applications.

Keywords:
Data anaylsisHypergraph regularizationNonnegative tensor decompositionTriple decomposition

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Area of Science:

  • Data Science
  • Machine Learning
  • Tensor Analysis

Background:

  • Tucker decomposition is vital for data representation but computationally expensive.
  • Bilevel triple decomposition (TriD) reduces computational cost but struggles with complex data manifolds.
  • Existing methods lack robust mechanisms for capturing intricate similarity relationships in tensor data.

Purpose of the Study:

  • To propose a novel hypergraph regularized nonnegative triple decomposition (TriD) for enhanced multiway data analysis.
  • To address the limitations of existing TriD methods in modeling complex data manifold structures.
  • To develop an efficient algorithm for solving the proposed decomposition model.

Main Methods:

  • Utilizing hypergraph learning to model complex relationships within raw data.
  • Developing a multiplicative update algorithm for optimization.
  • Theoretically proving the convergence of the proposed algorithm.

Main Results:

  • The proposed hypergraph regularized nonnegative TriD effectively captures complex data relationships.
  • The multiplicative update algorithm demonstrates convergence.
  • Extensive numerical tests on six real-world datasets confirm superior performance over state-of-the-art methods.

Conclusions:

  • The novel hypergraph regularized nonnegative TriD offers a powerful approach for multiway data analysis.
  • The method enhances the ability to model complex similarity structures in tensor data.
  • The findings suggest significant improvements in data representation and analysis accuracy.