Some Developments in Clustering Analysis on Stochastic Processes

Some Developments in Clustering Analysis on Stochastic Processes Qidi Peng Nan Rao † Ran Zhao ‡ Abstract We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the triangle inequality. Examples are provided when the processes are distribution ergodic, covariance ergodic and locally asymptotically self-similar, respectively. Keywords: stochastic process, unsupervised clustering, stationary ergodic processes, local asymptotic self-similarity 1 Introduction A stochastic process is an infinite sequence of random variables indexed by "time". The time indexes can be either discrete or continuous. Stochastic process type data have been broadly explored in biological and medical research (Damian et al., 2007; Zhao et al., 2014; J a askinen et al., 2014; et al., 2018).