Hyperbolic Distance Based on EMD and Diffusion for Hyperspectral Imaging

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.