Topological Eigenvalue Theorems for Tensor Analysis in Multi-Modal Data Fusion

• URL: http://arxiv.org/abs/2409.09392v2
• Date: Sat, 28 Sep 2024 13:39:14 GMT
• Title: Topological Eigenvalue Theorems for Tensor Analysis in Multi-Modal Data Fusion
• Authors: Ronald Katende,
• Abstract summary: This paper presents a novel framework for tensor eigenvalue analysis in the context of multi-modal data fusion. By establishing new theorems that link eigenvalues to topological features, the proposed framework provides deeper insights into the latent structure of data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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