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Advances in Self-Organizing Maps and Learning Vector Quantization pp 55–64Cite as

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

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Part of the Advances in Intelligent Systems and Computing book series (AISC,volume 295)

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.

Keywords

  • Multivariate time series
  • Nonlinear dimensionality reduction
  • Mapping distortion
  • Magnification Factors
  • Visualization
  • Generative Topographic Mapping
  • Variational Bayesian methods

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  • DOI: 10.1007/978-3-319-07695-9_5
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Author information

Authors and Affiliations

  1. Dept. de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona, 08034, Spain

    Alessandra Tosi & Alfredo Vellido

  2. Manchester Institute of Biotechnology, The University of Manchester, Manchester, M1 7DN, UK

    Iván Olier

Authors
  1. Alessandra Tosi
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  2. Iván Olier
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  3. Alfredo Vellido
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Applied Sciences Mittweida, Mittweida, Sachsen, Germany

    Thomas Villmann

  2. University of Applied Sciences Mittweida, Mittweida, Germany

    Frank-Michael Schleif

  3. University of Applied Sciences Mittweida, Mittweida, Germany

    Marika Kaden

  4. University of Applied Sciences Mittweida, Mittweida, Germany

    Mandy Lange

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Tosi, A., Olier, I., Vellido, A. (2014). Probability Ridges and Distortion Flows: Visualizing Multivariate Time Series Using a Variational Bayesian Manifold Learning Method. In: Villmann, T., Schleif, FM., Kaden, M., Lange, M. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 295. Springer, Cham. https://doi.org/10.1007/978-3-319-07695-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-07695-9_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07694-2

  • Online ISBN: 978-3-319-07695-9

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