提出可灵活比较张量的分解方法TULCA，提升复杂数据可视化分析能力。
Visual Analytics Using Tensor Unified Linear Comparative Analysis
- 将判别分析与对比学习结合，实现张量的灵活对比分解。
- 能从超算日志中提取核心张量并生成2D可视化结果。
- 适合需要深入分析多维数据结构的研究者使用。
比较张量并识别其（不）相似结构是理解复杂数据背后现象的基础。张量分解方法有助于提取张量的核心特征，支持张量的可视化分析。与仅适用于矩阵（即二阶张量）的降维方法不同，现有张量分解方法难以支持灵活的比较分析。为此，我们提出一种新的张量分解方法——张量统一线性对比分析（TULCA），通过扩展其降维对应方法ULCA来实现张量分析。TULCA融合判别分析与对比学习机制，支持张量间的灵活对比。我们还提出一种有效方法，将TULCA提取的核心张量转化为一组2D可视化图像。我们将TULCA功能集成至可视化分析界面，帮助分析师解读和优化结果。通过计算评估及两个案例研究（包括对超算日志的数据分析），验证了TULCA与可视化界面的有效性。
原文摘要 · Abstract (English)
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.
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