On the Number of Independent Components: An Adjusted Coefficient of Determination based Approach


Abstract


Independent Component Analysis (ICA) is a comparatively new statisticaland computational technique to find hidden components from multivariate statistical data. The technique is also employed as a tool for dimension reduction for efficient data analysis. Reduction in dimensions can be done byassigning ranks to the independent components in some appropriate way and then restricting the data analysis to certain high ranking components only.The problem of determining the number of high ranked ICs that should be retained is the main objective of this paper. A method based upon adjusted coefficient of determination is proposed for the purpose. The performance of the proposed method is demonstrated through experimental evaluation on real-world financial time series data.

DOI Code: 10.1285/i20705948v14n1p13

Keywords: Adjusted coefficient of determination; dimension reduction; financial time series; independent component analysis; multidimensional data; big data analytics

References


Afzal, S., & Iqbal, M. (2016). A new way to order independent components. Journal of Applied Statistics, 43.

Back, A. D., & Weigend, S. A. (1997). A first application of independent component Analysis to Extracting Structure from Stock Returns. International Jornal of Neural Systems, 8, 473-484.

Belouchrani, A., Meraim, K. A., Cardoso, J. F., & Moulines, E. (1997). A blind source separation technique based on second order statistics. IEEE Transactions on Signal Processing, 45, 434-444.

Bouveresse, D. J. R., González, A. M., Ammari, F., & Rutledge, D. N. (2012). Two novel methods for the determination of the number of components in independent components analysis models. Chemometrics and Intelligent Laboratory Systems, 112, 24-32.

Cardoso, J. F., & Souloumiac, A. (1993). Blind Beamforming for Non-Gaussian Signals. Radar and Signal Processing IEE Proceedings F, 140, 362-370.

Hyvärinen, A. (1999). Fast and robust fixedpoint algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10, 626-634.

Hyvärinen, A., & Oja, E. (1997). A fast fixed point algorithm for independent component analysis. Neural Computation, 9, 1483-1492.

Karhunen, J., Cichocki, A., Kasprzak, W., & Pajunen, P. (1997). On neural blind separation withnoise suppression and redundancy reduction. International Journal of Neural Systems, 8, 219-237.

Lee, S. M. (2003). Estimating the number of Independent Components via the SONIC Statistic. Oxford University, London, UK.

Prieto, E. G. (2011). Independent component analysis for time series. Charles III University of Madrid, Spain.

Roberts, S. (1998). Independent component analysis: Source assessment & separation, a Bayesian approach. IEE Proceedings Vision,Image &Signal Processing, 145.

Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society, 63, 411-423.

Wang, G., Cai, W., & Shao, X. (2006). A primary study on resolution of overlapping GC-MS signal using mean-field approach independent component analysis. Chemometrics and Intelligent Laboratory Systems, 82, 137-144.

Westad, F., & Kermit, M. (2003). Cross validation and uncertainty estimates in independent component analysis. Analytica Chimica Acta, 490, 341-354.


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