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Multivariate time-series analysis and diffusion maps

Publication ,  Journal Article
Lian, W; Talmon, R; Zaveri, H; Carin, L; Coifman, R
Published in: Signal Processing
April 25, 2015

Dimensionality reduction in multivariate time series analysis has broad applications, ranging from financial data analysis to biomedical research. However, high levels of ambient noise and various interferences result in nonstationary signals, which may lead to inefficient performance of conventional methods. In this paper, we propose a nonlinear dimensionality reduction framework using diffusion maps on a learned statistical manifold, which gives rise to the construction of a low-dimensional representation of the high-dimensional nonstationary time series. We show that diffusion maps, with affinity kernels based on the Kullback-Leibler divergence between the local statistics of samples, allow for efficient approximation of pairwise geodesic distances. To construct the statistical manifold, we estimate time-evolving parametric distributions by designing a family of Bayesian generative models. The proposed framework can be applied to problems in which the time-evolving distributions (of temporally localized data), rather than the samples themselves, are driven by a low-dimensional underlying process. We provide efficient parameter estimation and dimensionality reduction methodologies, and apply them to two applications: music analysis and epileptic-seizure prediction.

Duke Scholars

Published In

Signal Processing

DOI

ISSN

0165-1684

Publication Date

April 25, 2015

Volume

116

Start / End Page

13 / 28

Related Subject Headings

  • Networking & Telecommunications
  • 46 Information and computing sciences
  • 40 Engineering
  • 10 Technology
  • 09 Engineering
  • 08 Information and Computing Sciences
 

Citation

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Lian, W., Talmon, R., Zaveri, H., Carin, L., & Coifman, R. (2015). Multivariate time-series analysis and diffusion maps. Signal Processing, 116, 13–28. https://doi.org/10.1016/j.sigpro.2015.04.003
Lian, W., R. Talmon, H. Zaveri, L. Carin, and R. Coifman. “Multivariate time-series analysis and diffusion maps.” Signal Processing 116 (April 25, 2015): 13–28. https://doi.org/10.1016/j.sigpro.2015.04.003.
Lian W, Talmon R, Zaveri H, Carin L, Coifman R. Multivariate time-series analysis and diffusion maps. Signal Processing. 2015 Apr 25;116:13–28.
Lian, W., et al. “Multivariate time-series analysis and diffusion maps.” Signal Processing, vol. 116, Apr. 2015, pp. 13–28. Scopus, doi:10.1016/j.sigpro.2015.04.003.
Lian W, Talmon R, Zaveri H, Carin L, Coifman R. Multivariate time-series analysis and diffusion maps. Signal Processing. 2015 Apr 25;116:13–28.
Journal cover image

Published In

Signal Processing

DOI

ISSN

0165-1684

Publication Date

April 25, 2015

Volume

116

Start / End Page

13 / 28

Related Subject Headings

  • Networking & Telecommunications
  • 46 Information and computing sciences
  • 40 Engineering
  • 10 Technology
  • 09 Engineering
  • 08 Information and Computing Sciences