Hyperbolic Distance Based on EMD and Diffusion for Hyperspectral Imaging

Elad Lavi; Amir Bourvine; Ya-Wei Eileen Lin; Ronen Talmon

ICASSP 2025accepted0 citations

Hyperbolic Distance Based on EMD and Diffusion for Hyperspectral Imaging

Elad Lavi, Amir Bourvine, Ya-Wei Eileen Lin, Ronen Talmon

Abstract

In this paper, we introduce EMD-Based Hyperbolic Diffusion Distance (EMD-HDD), a new method for constructing a meaningful distance metric for hierarchical data with latent hierarchical structure. Our method relies on hyperbolic geometry, diffusion geometry, and the Earth Mover’s Distance (EMD). Specifically, our method embeds data points into a product manifold of hyperbolic spaces, allowing us to recover the hidden hierarchical structure encoded by the mutual relationships between features. We demonstrate the effectiveness of EMD-HDD through experiments on five hyperspectral imaging datasets, showcasing its capability to capture and reveal the intrinsic hierarchical structures inherent in such data.

BibTeX

@inproceedings{icassp2025_hyperbolicdistan,
  title = {Hyperbolic Distance Based on EMD and Diffusion for Hyperspectral Imaging},
  author = {Elad Lavi and Amir Bourvine and Ya-Wei Eileen Lin and Ronen Talmon},
  booktitle = {ICASSP 2025},
  year = {2025}
}