Static Models of Derivative-Coordinates Phase Spaces for Multivariate Time Series Classification: An Application to Signature Verification

Multivariate time series are sequences, whose order is provided by a time index; thus, most classifiers used on such data treat time as a special quantity, and encode it, structurally in a model. A typical example of such models is the hidden Markov model, where time is explicitely used to drive state transitions. The time information is discretised into a finite set of states, the, cardinality of which is largely chosen by empirical criteria. Taking as an example task signature verification. we propose an alternative approach using static probabilistic models of phase spaces, where the time information is preserved by embedding of the multivariate time series into a higher-dimensional and modelled probabilistically by using the theoretical framework of static Bayesian networks. We show empirically that, performance is equivalent to state-of-the-art signature verification systems.