Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization

TL;DR

This paper introduces spatially coherent clustering models based on orthogonal nonnegative matrix factorization with total variation regularization, improving clustering accuracy in spatially structured datasets like hyperspectral images.

Contribution

It proposes novel clustering models incorporating total variation regularization into orthogonal nonnegative matrix factorization, tailored for spatially coherent data.

Findings

Significantly improved clustering results on hyperspectral data

Effective integration of spatial coherence via TV regularization

Multiple optimization approaches demonstrated

Abstract

Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on orthogonal nonnegative matrix factorization, which include an additional total variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent postprocessing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of all proposed methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionisation imaging measurement, which leads to significantly better clustering results compared to classical clustering models.