Clustering piecewise stationary processes

The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary process. While stationary processes comprise one of the most general classes of processes in nonparametric statistics, and in particular, allow for arbitrary long-range dependencies, their key assumption of stationarity remains restrictive for some applications. We address this shortcoming by considering piecewise stationary processes, studied here for the first time in the context of clustering. It turns out that this problem allows for a rather natural definition of consistency of clustering algorithms. Efficient algorithms are proposed which are shown to be asymptotically consistent without any additional assumptions beyond piecewise stationarity. The theoretical results are complemented with experimental evaluations.