Generative Topographic Mapping (GTM) is a latent variable model that, in its standard version, was conceived to provide clustering and visualization of multivariate, real-valued, i.i.d. data. It was also extended to deal with non-i.i.d. data such as multivariate time series in a variant called GTM Through Time (GTMTT), defined as a constrained Hidden Markov Model (HMM). In this technical report, we provide the theoretical foundations of the reformulation of GTM-TT within the Variational Bayesian framework. This approach, in its application, should naturally handle the presence of noise in the time series, helping to avert the problem of data overfitting.
CitationOlier, I., Vellido, A. "A variational formulation for GTM through time: Theoretical foundations". 2007.
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