Probability Ridges and Distortion Flows: Visualizing Multivariate Time Series Using a Variational Bayesian Manifold Learning Method

Abstract

Abstract. Time-dependent natural phenomena and artificial processes can often be quantitatively expressed as multivariate time series (MTS). As in any other process of knowledge extraction from data, the analyst can benefit from the exploration of the characteristics of MTS through data visualization. This visualization often becomes difficult to interpret when MTS are modelled using nonlinear techniques. Despite their flexibility, nonlinear models can be rendered useless if such interpretability is lacking. In this brief paper, we model MTS using Variational Bayesian Generative Topographic Mapping Through Time (VB-GTM-TT), a variational Bayesian variant of a constrained hidden Markov model of the manifold learning family defined for MTS visualization. We aim to increase its interpretability by taking advantage of two results of the probabilistic definition of the model: the explicit estimation of probabilities of transition between states described in the visualization space and the quantification of the nonlinear mapping distortion.

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“…These prototypes are cluster centers and also the building elements of a mixture of distributions. In different variants, GTM has been used for missing data imputation (Vellido et al 2010) , outlier detection (Tosi and Vellido 2013), or time series analysis (Tosi et al 2014), as well as applied in areas such as medicine (Cruz and Vellido 2011)or e-learning (Etchells et al 2006), amongst others.…”