Multivariate Outlier Detection Using Independent Component Analysis

Md. Shamim Reza; Sabba Ruhi

doi:doi:10.11648/j.sjams.20150304.11

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Multivariate Outlier Detection Using Independent Component Analysis

Md. Shamim Reza, Sabba Ruhi

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 4)

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), 2024. Published by Science Publishing Group

Keywords

Kurtosis, Outlier, Independent Component Analysis, Normality

References

[1]	Atkinson, A. C., Riani, M., & Cerioli, A. (2004). Exploring multivariate data with the forward search. New York: Springer-Verlag.
[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.
[6]	Hogg, R.V. (1972),”More Light on the Kurtosis and Related Statistics,” Journal of the American Statistical Association, 67, 422-424.
[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.
[9]	J.C. Salagubang and Erniel B. Barrios, Outlier detection in high dimensional data in the context of clustering, 12th National Convention on Statistics (NCS) EDSA Shangri-La Hotel, Mandaluyong City October 1-2, 2013
[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.
[14]	Lihua An, S.Ejaz Ahmed. Improving the performance of kurtosis estimator. Computational Statistics and Data Analysis 52, 2669-2681. 2008.
[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.
[20]	Reza, M.S., Nasser, M. and Shahjaman, M. (2011) An Improved Version of Kurtosis Measure and Their Application in ICA, International Journal of Wireless Communication and Information Systems (IJWCIS) Vol 1 No 1.
[21]	Rousseeuw P.J., Van Zomeren B.C. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association. Vol. 85(411), pp. 633-651.
[22]	Scholz, M., Gatzek, S., Sterling, A., Fiehn, O., and Selbig, J. Metabolite fingerprinting: detecting biological features by independent component analysis. Bioinformatics 20, 2447-2454, 2004.

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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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TY  - JOUR
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

Md. Shamim Reza

Department of Mathematics, Pabna University of Science & Technology, Pabna, Bangladesh
Sabba Ruhi

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

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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  -

Copy | Download