Finite Element Approach to Clustering of Multidimensional Time Series

The authors present a new approach to clustering of time series based on a minimization of the averaged clustering functional. They demonstrate that for a fixed set of model parameters ... the appropriate Tykhonov-type regularization of this functional with some regularization factor ... results in a minimization problem similar to a variational problem usually associated with one-dimensional nonhomogeneous partial differential equations. They investigate the conditions under which the proposed scheme allows a monotone improvement of the initial parameter guess with respect to the minimization of the discretized version of the regularized functional. We also discuss the interpretation of the regularization factor in the Markovian case and show its connection to metastability and exit times. The computational performance of the resulting method is investigated numerically on multidimensional test data and is applied to the analysis of multidimensional historical stock market data. (ProQuest: ... denotes formulae/symbols omitted.)