Applied Math Talk: Cluster analysis on covariance stationary ergodic processes and locally asymptotically self-similar processes (Nan Rao, CGU)

We study the problems of clustering covariance stationary ergodic processes and locally asymptotically self-similar stochastic processes, when the true number of clusters is priorly known. A new covariance-based dissimilarity measure is introduced, from which efficient consistent clustering algorithms are obtained. As examples of application, clustering  fractional Brownian motions and clustering multifractional Brownian motions are respectively performed to illustrate the asymptotic consistency of the proposed algorithms.