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Multivariate Outlier Detection Using Independent Component Analysis

Received: 17 May 2015     Accepted: 29 May 2015     Published: 19 June 2015
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Abstract

The recent developments by considering a rather unexpected application of the theory of Independent component analysis (ICA) found in outlier detection, data clustering and multivariate data visualization etc. Accurate identification of outliers plays an important role in statistical analysis. If classical statistical models are blindly applied to data containing outliers, the results can be misleading at best. In addition, outliers themselves are often the special points of interest in many practical situations and their identification is the main purpose of the investigation. This paper takes an attempt a new and novel method formultivariate outlier detection using ICA and compares with different outlier detection techniques in the literature.

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 4)
DOI 10.11648/j.sjams.20150304.11
Page(s) 171-176
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Kurtosis, Outlier, Independent Component Analysis, Normality

References
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[2] Balanda KP, MacGillivray HL (1988), Kurtosis a critical review. Journal of the American Statistical Association, 42,111-119.
[3] Barnett, V, & Lewis, T. (1994). Outliers in statistical data (3rd ed.). New York: Wiley.
[4] Groeneveld RA (1998) A class of quantile measures for kurtosis. Am Stat 52: 325-329.
[5] Hawkins, D.M. (1980). Identification of outliers. London: Chapman and Hall.
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[7] Huber PJ (1981) robust statistics. Wiley, London.
[8] Hyv¨arinen, A. and Oja, E.: Independent component analysis: Algorithms and applications. Neural Networks. 4-5(13):411-430. 2000.
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[10] Johnson, R. and Wischern, D. (2002). Applied Multivariate statistical analysis, 5th ed. Prentice-Hall, Inc.
[11] Jones, M. and Sibson, R. What is projection pursuit? J. of the Royal Statistical Society, Ser. A, 150:1-36. 1987.
[12] Kim TH, White H (2003) On more robust estimation of skewness and kurtosis: simulation and application to the S&P500 index. Department of Economics, UCSD, Paper 2003-12.
[13] Kotz, S., and Seier, E. (2008), Kurtosis of the Two-Sided Power Distribution, Brazilian Journal of Probability and Statistics, 28, 6168.
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[15] Matthias Scholz, Yves Gibon, Mark Stitt and Joachim Selbig, Independent component analysis of starch deficient pgm mutants. Proceedings of the German conference on Bioinformatics. Gesellschaft fur info mark, Bonn, pp.95-104, 2004.
[16] Maurya V.N., Misra R.B., Jaggi C.K., and Maurya A.K., Performance analysis of powers of skewness and kurtosis based multivariate normality tests and use of extended Monte Carlo simulation for proposed novelty algorithm, American Journal of Theoretical and Applied Statistics, Science Publishing Group, USA, Vol. 4(2-1), pp. 11-18, 2015.
[17] Maurya V. N., Misra R. B., Jaggi Chadra K., Maurya A. K. and Arora D. K., Design and estimate of the optimal parameters of adaptive control chart model using Markov chains technique, Special Issue: Scope of Statistical Modeling and Optimization Techniques in Management and Decision Making Process, American Journal of Theoretical and Applied Statistics, Science Publishing Group, USA, 2014.
[18] Moors, J. J. A. (1988), ”A Quantile Alternative for Kurtosis,” The Statistician, 37, 25-32.
[19] Pearson K (1905) Skew variation, a rejoinder. Biometrika 4:169212.
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  • APA Style

    Md. Shamim Reza, Sabba Ruhi. (2015). Multivariate Outlier Detection Using Independent Component Analysis. Science Journal of Applied Mathematics and Statistics, 3(4), 171-176. https://doi.org/10.11648/j.sjams.20150304.11

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    ACS Style

    Md. Shamim Reza; Sabba Ruhi. Multivariate Outlier Detection Using Independent Component Analysis. Sci. J. Appl. Math. Stat. 2015, 3(4), 171-176. doi: 10.11648/j.sjams.20150304.11

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    AMA Style

    Md. Shamim Reza, Sabba Ruhi. Multivariate Outlier Detection Using Independent Component Analysis. Sci J Appl Math Stat. 2015;3(4):171-176. doi: 10.11648/j.sjams.20150304.11

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  • @article{10.11648/j.sjams.20150304.11,
      author = {Md. Shamim Reza and Sabba Ruhi},
      title = {Multivariate Outlier Detection Using Independent Component Analysis},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {3},
      number = {4},
      pages = {171-176},
      doi = {10.11648/j.sjams.20150304.11},
      url = {https://doi.org/10.11648/j.sjams.20150304.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150304.11},
      abstract = {The recent developments by considering a rather unexpected application of the theory of Independent component analysis (ICA) found in outlier detection, data clustering and multivariate data visualization etc. Accurate identification of outliers plays an important role in statistical analysis. If classical statistical models are blindly applied to data containing outliers, the results can be misleading at best. In addition, outliers themselves are often the special points of interest in many practical situations and their identification is the main purpose of the investigation. This paper takes an attempt a new and novel method formultivariate outlier detection using ICA and compares with different outlier detection techniques in the literature.},
     year = {2015}
    }
    

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    T1  - Multivariate Outlier Detection Using Independent Component Analysis
    AU  - Md. Shamim Reza
    AU  - Sabba Ruhi
    Y1  - 2015/06/19
    PY  - 2015
    N1  - https://doi.org/10.11648/j.sjams.20150304.11
    DO  - 10.11648/j.sjams.20150304.11
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 171
    EP  - 176
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20150304.11
    AB  - The recent developments by considering a rather unexpected application of the theory of Independent component analysis (ICA) found in outlier detection, data clustering and multivariate data visualization etc. Accurate identification of outliers plays an important role in statistical analysis. If classical statistical models are blindly applied to data containing outliers, the results can be misleading at best. In addition, outliers themselves are often the special points of interest in many practical situations and their identification is the main purpose of the investigation. This paper takes an attempt a new and novel method formultivariate outlier detection using ICA and compares with different outlier detection techniques in the literature.
    VL  - 3
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, Pabna University of Science & Technology, Pabna, Bangladesh

  • Department of Mathematics, Pabna University of Science & Technology, Pabna, Bangladesh

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