Statistical Independence and Independent Component Analysis

Abstract:

Independent Component Analysis (ICA) is a recent method of blind source separation, it has been employed in medical image processing and structural damge detection. It can extract source signals and the unmixing matrix of the system using mixture signals only. This novel method relies on the assumption that source signals are statistically independent. This paper looks at various measures of statistical independence (SI) employed in ICA, the measures proposed by Bakirov and his associates, and the effects of levels of SI of source signals on the output of ICA. Firstly, two statistical independent signals in the form of uniform random signals and a mixing matrix were used to simulate mixture signals to be anlysed by fastICA package, secondly noise was added onto the signals to investigate effects of levels of SI on the output of ICA in the form of soure signals, the mixing and unmixing matrix. It was found that for p-value given by Bakirov’s SI statistical testing of the null hypothesis H₀ is a good indication of the SI between two variables and that for p-value larger than 0.05, fastICA performs satisfactorily.

• Periodical: Applied Mechanics and Materials (Volume 553)
• Pages: 564-569
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.553.564
• Online since: May 2014
• Authors: Yaseen Unnisa*, Danh Tran, Fu Chun Huang
• Keywords: Bakirov’s Indep. Test, Blind Source Separation, Fastica, Independent Component Analysis (ICA), Statistical Independence, Structural Damage Detection

References

[1] P. Comon and C. Jutten, Handbook of Blind Source Separation, Independent Component analysis and Applications, Academic Press, Amsterdam, (2010).

[2] A. Hyvӓrinen , J. Karhunen and E. Oja, Independent Component Analysis, Wiley, New York, (2001).

[3] C. Zang, M.I. Friswell and M. Imregun, Structural Damage Detection using Independent Component Analysis, Structural Health Monitoring, 3(1) (2004) 69-83.

DOI: 10.1177/1475921704041876

[4] W. Zhou and D. Chelidze, Blind source separate based vibration mode identification, Mechanical Systems and Signal Processing, 21 (2007) 3072-3087.

DOI: 10.1016/j.ymssp.2007.05.007

[5] C Junhong and W. Zhuobin, Independent component analysis in frequency domain and its application in structural vibration signal separation, Procedia Engineering 16 (2011) 511-517.

DOI: 10.1016/j.proeng.2011.08.1118

[6] http: /research. ics. aalto. fi/ica/cocktail/cocktail_en. cgi.

[7] T. Hastie, R. Tibshirani and J. Friedman, The elements of statistical learning, data mining, inference and prediction, Second Edition, Springer, (2008).

DOI: 10.1111/j.1751-5823.2009.00095_18.x

[8] A. Hyvӓrinen and E. Oja, Independent component analysis: algorithms and applications, Neural Networks, 13 (2000) 411-430.

DOI: 10.1016/s0893-6080(00)00026-5

[9] http: /cran. r-project. org/web/packages/fastICA/fastICA. pdf.

[10] N.A. Weiss, Introductory Statistics, 7th edition, Pearson, 2005, Boston.

[11] J. V. Stone, Independent Component Analysis, a tutorial introduction, The MIT Press, Massachusetts, (2004).

[12] S. S. Wilks, On the independence of k sets of normally distributed statistical variable, Econometrica, Vol. 3, No. 3 (1935) 309-326.

DOI: 10.2307/1905324

[13] N. K. Bakirov, M. L. Rizzo, and G. J. Szekely, A multivariate non-parametric test of independence, Journal of Multivariate Analysis, 97 (2006) 1742-1756.

DOI: 10.1016/j.jmva.2005.10.005

[14] G. J. Szekely, M. L. Rizzo and N. K. Bakirov, Measuring and testing dependence by correlation of distances, Journal of The Annals of Statistics, 35, 6 (2007) 2769–2794.

[15] http: /cran. r-project. org/web/packages/energy/index. html.