  Clustering is an unsupervised learning technique that is useful when working
with a large volume of unlabeled data. Complex dynamical systems in real life
often entail data streaming from a large number of sources. Although it is
desirable to use all source variables to form accurate state estimates, it is
often impractical due to large computational power requirements, and
sufficiently robust algorithms to handle these cases are not common. We propose
a hierarchical time series clustering technique based on symbolic dynamic
filtering and Granger causality, which serves as a dimensionality reduction and
noise-rejection tool. Our process forms a hierarchy of variables in the
multivariate time series with clustering of relevant variables at each level,
thus separating out noise and less relevant variables. A new distance metric
based on Granger causality is proposed and used for the time series clustering,
as well as validated on empirical data sets. Experimental results from
occupancy detection and building temperature estimation tasks show fidelity to
the empirical data sets while maintaining state-prediction accuracy with
substantially reduced data dimensionality.
