Covariance-based Dissimilarity Measures Applied to Clustering Wide-sense Stationary Ergodic Processes

TL;DR

This paper proposes a novel covariance-based dissimilarity measure and algorithms for clustering wide-sense stationary ergodic processes, with applications demonstrated on synthetic and real-world data.

Contribution

It introduces a new clustering approach for wide-sense stationary ergodic processes using covariance-based dissimilarity measures and provides algorithms for both offline and online datasets.

Findings

Effective clustering of synthetic data demonstrated.

Application to real-world data shows practical utility.

Discussion on improving clustering efficiency for specific process types.

Abstract

We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure together with asymptotically consistent algorithms is designed for clustering offline and online datasets, respectively. We also suggest a formal criterion on the efficiency of dissimilarity measures, and discuss of some approach to improve the efficiency of our clustering algorithms, when they are applied to cluster particular type of processes, such as self-similar processes with wide-sense stationary ergodic increments. Clustering synthetic data and real-world data are provided as examples of applications.