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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References
Balzi, A., Yger, F., Sugiyama, M.: Importance-weighted covariance estimation for robust common spacial pattern. Pattern Recogn. Lett. 68, 139–145 (2015)
Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algorithms. Springer, New York (1981)
Breloy, A., Ginolhac, G., et al.: Robust covariance matrix estimation in heterogeneous low rank context. IEEE Trans. Sig. Process. 64(22), 5794–5805 (2016)
Duda, R., Hart, P., Stork, D.: Pattern Classification. Wiley, New York (2000)
Guru, D., Suraj, M., Manjunath, S.: Fusion of covariance matrices of PCA and FLD. Pattern Recogn. Lett. 32(3), 432–440 (2011)
He, R., Hu, B.G., et al.: Robust principal component analysis based on maximum correntropy criterion. IEEE Trans. Image Process. 20(6), 1485–1494 (2011)
Honeine, P.: Online kernel principal component analysis: a reduced-order model. IEEE Trans. Pattern Anal. Mach. Intell. 34(9), 1814–1826 (2011)
Huber, P.: Robust Statistics. Wiley, New Jersey (1982)
Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (2004)
Liang, Z., Xia, S., et al.: Feature extraction based on Lp-norm generalized principal component analysis. Pattern Recogn. Lett. 34(9), 1037–1045 (2013)
Oh, J., Kwak, N.: Generalized mean for robust principal component analysis. Pattern Recogn. 54(C), 116–127 (2016)
Schreiber, T., Kaplan, D.: Nonlinear noise reduction for electrocardiograms. Chaos: Interdisc. J. Nonlinear Sci. 6(1), 87–92 (1996)
Verboven, S., Huber, M.: LIBRA: a MATLAB library for robust analysis. Chemometr. Intell. Lab. Syst. 75(2), 127–136 (2005)
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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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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DOI: https://doi.org/10.1007/978-3-319-67792-7_24
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