$k$-means on Positive Definite Matrices, and an Application to Clustering in Radar Image Sequences

TL;DR

This paper explores $k$-means clustering for Symmetric Positive Definite matrices in a non-Euclidean space, and applies it to cluster radar image pixel time-series using autocovariance matrices.

Contribution

It introduces theoretical properties of $k$-means for SPD matrices and demonstrates its application to radar image sequence clustering.

Findings

Theoretical properties for $k$-means on SPD matrices are established.

Effective clustering of radar image pixels using autocovariance matrices is demonstrated.

Method provides a natural representation for non-Euclidean data.

Abstract

We state theoretical properties for $k$-means clustering of Symmetric Positive Definite (SPD) matrices, in a non-Euclidean space, that provides a natural and favourable representation of these data. We then provide a novel application for this method, to time-series clustering of pixels in a sequence of Synthetic Aperture Radar images, via their finite-lag autocovariance matrices.