Multivariate Outlier Detection Using Independent Component Analysis
Science Journal of Applied Mathematics and Statistics
Volume 3, Issue 4, August 2015, Pages: 171-176
Received: May 17, 2015; Accepted: May 29, 2015; Published: Jun. 19, 2015
Views 5459      Downloads 231
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
Article Tools
Follow on us
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.
Kurtosis, Outlier, Independent Component Analysis, Normality
To cite this article
Md. Shamim Reza, Sabba Ruhi, Multivariate Outlier Detection Using Independent Component Analysis, Science Journal of Applied Mathematics and Statistics. Vol. 3, No. 4, 2015, pp. 171-176. doi: 10.11648/j.sjams.20150304.11
Atkinson, A. C., Riani, M., & Cerioli, A. (2004). Exploring multivariate data with the forward search. New York: Springer-Verlag.
Balanda KP, MacGillivray HL (1988), Kurtosis a critical review. Journal of the American Statistical Association, 42,111-119.
Barnett, V, & Lewis, T. (1994). Outliers in statistical data (3rd ed.). New York: Wiley.
Groeneveld RA (1998) A class of quantile measures for kurtosis. Am Stat 52: 325-329.
Hawkins, D.M. (1980). Identification of outliers. London: Chapman and Hall.
Hogg, R.V. (1972),”More Light on the Kurtosis and Related Statistics,” Journal of the American Statistical Association, 67, 422-424.
Huber PJ (1981) robust statistics. Wiley, London.
Hyv¨arinen, A. and Oja, E.: Independent component analysis: Algorithms and applications. Neural Networks. 4-5(13):411-430. 2000.
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
Johnson, R. and Wischern, D. (2002). Applied Multivariate statistical analysis, 5th ed. Prentice-Hall, Inc.
Jones, M. and Sibson, R. What is projection pursuit? J. of the Royal Statistical Society, Ser. A, 150:1-36. 1987.
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.
Kotz, S., and Seier, E. (2008), Kurtosis of the Two-Sided Power Distribution, Brazilian Journal of Probability and Statistics, 28, 6168.
Lihua An, S.Ejaz Ahmed. Improving the performance of kurtosis estimator. Computational Statistics and Data Analysis 52, 2669-2681. 2008.
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.
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.
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.
Moors, J. J. A. (1988), ”A Quantile Alternative for Kurtosis,” The Statistician, 37, 25-32.
Pearson K (1905) Skew variation, a rejoinder. Biometrika 4:169212.
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.
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.
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.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186