Visual Analytics Using Tensor Unified Linear Comparative Analysis

2025-07-26

AI Summary

Existing tensor decomposition methods lack flexible capabilities for comparing structural similarities and differences across multiple tensors, hindering interpretable high-dimensional pattern analysis. To address this, we propose TULCA—the first framework extending Unified Linear Comparison Analysis (ULCA) to higher-order tensors—integrating tensor decomposition, discriminant analysis, and contrastive learning to enable structure-aware tensor alignment and quantitative difference measurement. We design a structure-preserving 2D projection algorithm for core tensors and develop an interactive visual analytics interface. Evaluated on real-world datasets including supercomputing system logs, TULCA significantly improves inter-tensor similarity discrimination accuracy and interpretability. It supports dynamic feedback-driven optimization and efficient pattern recognition, establishing a novel paradigm for comparative analysis of complex multidimensional data.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Video Understanding & Activity Analysis
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Comparing tensors to identify their dissimilar structures
• Extending ULCA for flexible tensor decomposition analysis
• Visualizing core tensor data in 2D for analytics

Innovation

• Extends ULCA for tensor decomposition
• Integrates discriminant and contrastive learning
• Visualizes core tensor in 2D