Covariance-based Dissimilarity Measures Applied to Clustering Wide-sense Stationary Ergodic Processes
This addresses a novel unsupervised learning problem for analyzing stochastic processes, though it appears incremental in extending clustering methods to this specific domain.
The paper tackles the problem of clustering wide-sense stationary ergodic stochastic processes by introducing covariance-based dissimilarity measures and asymptotically consistent algorithms for offline and online datasets, with applications demonstrated on synthetic and real-world data.
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.