Visualizing States of Time-Series Data by Autoregressive Gaussian Process Dynamical Models

Abstract

Gaussian process dynamical models (GPDMs) are used for nonlinear dimensionality reduction in time series by means of Gaussian process priors. An extension of GPDMs is proposed for visualizing the states of time series. The conventional GPDM approach associates a state with an observation value. Therefore, observations changing over time cannot be represented by a single state. Consequently, the resulting visualization of state transition is difficult to understand, as states change when the observation values change. To overcome this issue, autoregressive GPDMs, called ARGPDMs, are proposed. They associate a state with a vector autoregressive (VAR) model. Therefore, observations changing over time can be represented by a single state. The resulting visualization is easier to understand, as states change only when the VAR model changes. We demonstrate experimentally that the ARGPDM approach provides better visualization compared with conventional GPDMs.