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    Area of Science:

    • Data Science
    • Machine Learning
    • Scientific Computing

    Background:

    • Comparing tensor structures is crucial for understanding complex data.
    • Existing tensor decomposition methods lack flexible comparative analysis capabilities.
    • Dimensionality reduction methods are limited to matrix analysis.

    Purpose of the Study:

    • Introduce a novel tensor decomposition method, TULCA, for flexible tensor comparison.
    • Extend the ULCA (Unified Linear Comparative Analysis) method for tensor analysis.
    • Develop a visual analytics interface for TULCA results.

    Main Methods:

    • Developed TULCA by extending ULCA for tensor decomposition.
    • Integrated discriminant analysis and contrastive learning into TULCA.
    • Created a method for visualizing core tensors into 2D representations.

    Main Results:

    • TULCA enables flexible and comparative analysis of tensors.
    • The visual analytics interface aids in interpreting TULCA results.
    • Demonstrated TULCA's efficacy through computational evaluations and case studies.

    Conclusions:

    • TULCA provides a powerful new tool for tensor decomposition and comparative analysis.
    • The integrated visualization enhances the interpretability of tensor structures.
    • TULCA is effective for analyzing complex datasets, such as supercomputer log data.