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Smooth Projective Noise Reduction for Nonlinear Time Series

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Topics in Nonlinear Dynamics, Volume 1

Part of the book series: Conference Proceedings of the Society for Experimental Mechanics Series ((CPSEMS,volume 35))

Abstract

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Locally projective noise reduction using proper orthogonal decomposition (POD) is one of the most effective tools. It works for both map-like and continuously sampled time series. However, it only looks at geometrical or topological properties of data and does not take into account temporal characteristics of time series. Here we present a new noise reduction method using smooth orthogonal decomposition (SOD) of bundles of locally reconstructed trajectory strands, which imposes temporal smoothness on the filtered time series. It is shown that SOD based noise reduction significantly outperforms the POD based method for the continuously sampled noisy time series.

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Notes

  1. 1.

    Concept similar to SOD called slow feature analysis has been used for pattern analysis in neural science [19–26].

  2. 2.

    You may want to use sod of individual strands to get several samples of smooth subspace basis, and then apply sod to the matrix collecting all the basis to find the dimensionality of global bases.

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Acknowledgements

This paper is based upon work supported by the National Science Foundation under Grant No. 1100031.

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Authors and Affiliations

  1. Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, 92 Upper College Road, Kingston, RI, 02881, USA

    David Chelidze

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  1. David Chelidze
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Correspondence to David Chelidze .

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Editors and Affiliations

  1. University of Liege, Place du 20-Août 7, Liege, 4000, Belgium

    Gaetan Kerschen

  2. , School of Mechanical Engineering, Purdue University, Purdue Mall 585, West Lafayette, 47907-2088, USA

    Douglas Adams

  3. LMS International, Brussels, Belgium

    Alex Carrella

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Chelidze, D. (2013). Smooth Projective Noise Reduction for Nonlinear Time Series. In: Kerschen, G., Adams, D., Carrella, A. (eds) Topics in Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6570-6_6

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  • DOI: https://doi.org/10.1007/978-1-4614-6570-6_6

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