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Cross-Modal Multivariate Pattern Analysis
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Multilinear Common Component Analysis via Kronecker Product Representation.

Kohei Yoshikawa1, Shuichi Kawano2

  • 1Graduate School of Informatics and Engineering, The University of Electro-Communications, Chofu-shi, Tokyo 182-8585, Japan yoshikawa.kohei615@gmail.com.

Neural Computation
|July 19, 2021
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Summary
This summary is machine-generated.

This study introduces multilinear common component analysis (MCCA) to find shared structures in multiple tensor datasets. MCCA effectively extracts common bases, preserving essential information from complex data.

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Area of Science:

  • Multivariate statistics
  • Data mining
  • Machine learning

Background:

  • Extracting common structures from multiple datasets is challenging.
  • Tensor data analysis requires specialized techniques.
  • Existing methods may not efficiently capture shared information across tensors.

Purpose of the Study:

  • To propose a novel method for extracting common structures from multiple tensor datasets.
  • To develop multilinear common component analysis (MCCA) for this purpose.
  • To ensure the method preserves essential information from the data.

Main Methods:

  • Multilinear Common Component Analysis (MCCA) is proposed.
  • The method utilizes Kronecker products of mode-wise covariance matrices.
  • An estimation algorithm guaranteeing mode-wise global convergence is developed.

Main Results:

  • MCCA successfully constructs a common basis from multiple tensor datasets.
  • The common basis retains significant information from the original data.
  • Numerical studies demonstrate the effectiveness of the MCCA approach.

Conclusions:

  • MCCA is an effective technique for common structure extraction in tensor data.
  • The proposed estimation algorithm ensures reliable and convergent results.
  • This method offers a valuable tool for analyzing multi-tensor datasets.