Finite Element Approach to Clustering of Multidimensional Time Series

Abstract

We present a new approach to clustering of time series based on a minimization of the averaged clus- tering functional. The proposed functional describes the mean distance between observation data and its representation in terms of K abstract models of a certain predefined class (not necessarily given by some probability distribution). For a fixed time series x(t) this functional depends on K sets of model parameters  = (θ1, . . . , θK) and K functions of cluster affiliations