Abstract
The GTM (Generative Topographic Mapping) algorithm was introduced by Bishop et al. as a probabilistic re-formulation of the self-organizing map (SOM). The GTM algorithm captures the structure of data
by modeling the data distribution in terms of nonlinear transformation from latent variables to data space, and which is used as a data visualization tool. The object of this paper is to visualize time series data using GTM. The standard GTM algorithm assumes that
the data are independent and identically distributed samples. For time series, however, the i.i.d. assumption is a poor approximation. In this paper we propose the extension of the GTM to handle time series, which we call the GTM-ARHMM algorithm, by assuming that the time series is generated by an Auto-Regressive Hidden Markov Model (ARHMM).
