A Variational Formulation for GTM Through Time: Theoretical Foundations
نویسندگان
چکیده
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.
منابع مشابه
A Variational Bayesian Formulation for GTM: Theoretical Foundations
Generative Topographic Mapping (GTM) is a non-linear latent variable model of the manifold learning family that provides simultaneous visualization and clustering of high-dimensional data. It was originally formulated as a constrained mixture of Gaussian distributions, for which the adaptive parameters were determined by Maximum Likelihood (ML), using the Expectation-Maximization (EM) algorithm...
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