Linguistically Described Covariance Matrix Estimation (original) (raw)

Abstract

In this paper we present a covariance matrix estimation method based on linguistically described data samples. The linguistic variable describes a real data samples that could be used for a calculation of the covariance matrix. In most cases, real dataset contains noise samples that manifest as outliers. Hence, the covariance matrix estimation problem can be formulated in the following way: take only these data samples that are not outliers. In this way, the influence of outliers is confined and thereby increases the robustness of the estimation. Linguistic variable distance takes values that are fuzzy sets. In the simplest case, the distance can be small or large. The distance is calculated between the data samples and the dataset center. In this paper we used generalized sample mean estimator for the calculation of the dataset center. The proposed method was used in the nonlinear state-space projection method (NSSP) where the estimation of a covariance matrix plays crucial role. The modified NSSP method was applied to ECG signal processing.

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Acknowledgements

This research was supported by statutory funds (BK-2017) of the Institute of Electronics, Silesian University of Technology. The work was performed using the infrastructure supported by POIG.02.03.01-24-099/13 grant: GeCONiI—Upper Silesian Center for Computational Science and Engineering.

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Authors and Affiliations

  1. Faculty of Automatic Control, Electronics and Computer Science, Institute of Electronics, Silesian University of Technology, Gliwice, Poland
    Tomasz Przybyła & Tomasz Pander

Authors

  1. Tomasz Przybyła
  2. Tomasz Pander

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Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland
    Aleksandra Gruca
  2. Institute of Informatics, Silesian University of Technology, Gliwice, Poland
    Tadeusz Czachórski
  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland
    Katarzyna Harezlak
  4. Institute of Informatics, Silesian University of Technology, Gliwice, Poland
    Stanisław Kozielski
  5. Institute of Informatics, Silesian University of Technology, Gliwice, Poland
    Agnieszka Piotrowska

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Przybyła, T., Pander, T. (2018). Linguistically Described Covariance Matrix Estimation. In: Gruca, A., Czachórski, T., Harezlak, K., Kozielski, S., Piotrowska, A. (eds) Man-Machine Interactions 5. ICMMI 2017. Advances in Intelligent Systems and Computing, vol 659. Springer, Cham. https://doi.org/10.1007/978-3-319-67792-7\_24

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