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

arXiv: https://arxiv.org/abs/2409.09392 · HTML: https://mlsanity.com/paper/2409.09392/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 14 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion](https://mlsanity.com/paper/2006.10657/) (2020)
- [Integrated Construction of Multimodal Atlases with Structural Connectomes in the Space of Riemannian Metrics](https://mlsanity.com/paper/2109.09808/) (2021)

## Abstract (arXiv)

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.