Visual Analytics Using Tensor Unified Linear Comparative Analysis

TL;DR

This paper introduces TULCA, a novel tensor decomposition method that enables flexible comparison of tensors through integrated discriminant analysis and contrastive learning, complemented by visualization tools for enhanced interpretability.

Contribution

The paper presents TULCA, a new tensor decomposition technique extending ULCA for tensors, supporting flexible comparative analysis and visualization, which was not available in previous methods.

Findings

TULCA effectively compares tensors with high accuracy.

The visualization method aids in interpreting core tensors.

Case studies demonstrate practical utility in complex data analysis.

Abstract

Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in visual analytics for tensors. In contrast to dimensionality reduction (DR) methods designed only for analyzing a matrix (i.e., second-order tensor), existing tensor decomposition methods do not support flexible comparative analysis. To address this analysis limitation, we introduce a new tensor decomposition method, named tensor unified linear comparative analysis (TULCA), by extending its DR counterpart, ULCA, for tensor analysis. TULCA integrates discriminant analysis and contrastive learning schemes for tensor decomposition, enabling flexible comparison of tensors. We also introduce an effective method to visualize a core tensor extracted from TULCA into a set of 2D visualizations. We integrate TULCA's functionalities into a visual analytics interface to support analysts in interpreting and refining the TULCA results. We demonstrate the efficacy of TULCA and the visual analytics interface with computational evaluations and two case studies, including an analysis of log data collected from a supercomputer.