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

TL;DR

This paper introduces a topological approach to tensor eigenvalue analysis for multi-modal data fusion, linking eigenvalues to topological invariants to improve interpretability and robustness in data analysis.

Contribution

It develops new theorems connecting tensor eigenvalues with topological features, offering a novel perspective beyond traditional matrix-based methods.

Findings

Enhanced understanding of tensor structures through topological invariants

Improved interpretability and robustness in data fusion applications

Theoretical and practical validation in machine learning contexts

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.