# Spectral-Spatial Diffusion Geometry for Hyperspectral Image Clustering

## TL;DR

This paper introduces a spectral-spatial diffusion geometry method for hyperspectral image clustering that leverages spatial regularization to improve clustering accuracy and computational efficiency.

## Contribution

It proposes a novel unsupervised clustering algorithm that incorporates spatial regularity into diffusion processes for hyperspectral images, enhancing performance over existing methods.

## Key findings

- Outperforms state-of-the-art clustering algorithms on real hyperspectral data.
- Provides a computationally efficient approach with low complexity.
- Spatial regularization improves clustering accuracy.

## Abstract

An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone. The regularized diffusion process is subsequently used to embed the high-dimensional HSI into a lower dimensional space through diffusion distances. Cluster modes are computed using density estimation and diffusion distances, and all other points are labeled according to these modes. The proposed method has low computational complexity and performs competitively against state-of-the-art HSI clustering algorithms on real data. In particular, the proposed spatial regularization confers an empirical advantage over non-regularized methods.