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

We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure and consistent algorithms are designed for clustering offline and online data settings, respectively. We also suggest a formal criterion on the efficiency of dissimilarity measures, and discuss of some approach to improve the efficiency of 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 sampled from fractional Brownian motions is provided as an example of application.