Visual Analytics using Tensor Unified Linear Comparative Analysis

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.