用拓扑特性分析多模态数据张量，提升结构可解释性。
Topological Eigenvalue Theorems for Tensor Analysis in Multi-Modal Data Fusion
- 引入贝蒂数等拓扑不变量，建立张量特征值与拓扑结构的关联
- 理论证明特征值分布与数据拓扑结构直接相关
- 适合关注数据深层结构的机器学习与融合分析研究者
本文提出一种新型张量特征值分析框架，用于多模态数据融合，利用贝蒂数等拓扑不变量。传统张量特征值方法多基于矩阵理论延伸，而本工作从拓扑视角出发，建立特征值与拓扑特征的新定理，深化对数据潜在结构的理解，显著提升模型的可解释性与鲁棒性。在数据融合应用中验证了该方法的理论价值与实际效果，具有广泛影响潜力。
原文摘要 · Abstract (English)
This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion, leveraging topological invariants such as Betti numbers. Traditional approaches to tensor eigenvalue analysis often extend matrix theory, whereas this work introduces a topological perspective to enhance the understanding of tensor structures. By establishing new theorems that link eigenvalues to topological features, the proposed framework provides deeper insights into the latent structure of data, improving both interpretability and robustness. Applications in data fusion demonstrate the theoretical and practical significance of this approach, with potential for broad impact in machine learning and data science.
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