Visualizing states in autoregressive hidden Markov models using generative topographic mapping

The generative topographic mapping (GTM) algorithm was proposed as a probabilistic re-formulation of the self-organizing map (SOM). The GTM algorithm captures the structure of data by modeling the data with a nonlinear transformation from low-dimensional latent variable space to multidimensional data space, and which can be used as a visualization tool. The object of this paper is to extend the GTM algorithm to deal with multivariate time series. The standard GTM algorithm assumes that the data are independent and identically distributed samples. However, the i.i.d. assumption is clearly inappropriate for time series. In this paper we propose the extension of the GTM for multivariate time series, which we call GTM-ARHMM, by assuming that the time series is generated by autoregressive hidden Markov models (ARHMMs).