Abstract
Charrelation matrices are a generalization of the covariance matrix, encompassing statistical information beyond second order while maintaining a convenient 2-dimensional structure. In the context of ICA, charrelation matrices-based separation was recently shown to potentially attain superior performance over commonly used methods. However, this approach is strongly dependent on proper selection of the parameters (termed processing-points) which parameterize the charrelation matrices. In this work we derive a data-driven criterion for proper selection of the set of processing-points. The proposed criterion uses the available mixtures samples to quantify the resulting separation errors’ covariance matrix in terms of the processing points. Minimizing the trace of this matrix with respect to the processing points enables to optimize (asymptotically) the selection of these points, thereby yielding better separation results than other methods, as we demonstrate in simulation.
This research was supported by the Israeli Science Foundation (grant No. 1255/08).
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References
Cardoso, J.-F., Souloumiac, A.: Blind beamforming for non-Gaussian signals. IEE Proc.-F. 140(6), 362–370 (1993)
Belouchrani, A., Abed-Meraim, K., Cardoso, J.-F., Moulines, E.: A blind source separation technique using second-order statistics. IEEE Trans. Signal Processing 45, 434–444 (1997)
Pham, D.-T., Cardoso, J.-F.: Blind separation of instantaneous mixtures of non stationary sources. IEEE Trans. on Signal Processing 49(9), 1837–1848 (2001)
Slapak, A., Yeredor, A.: Weighting for more. Enhancing Characteristic-Function Based ICA with Asymptotically Optimal Weighting. Sig. Process. 91(8), 2016–2027 (2011)
Hyvr̈inen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Comp. 9(7), 1483–1492 (1997)
Koldovský, Z., Tichavský, P., Oja, E.: Efficient variant of algorithm FastICA for independent component analysis attaining the Cramér-Rao lower bound. IEEE Trans. on Neural Networks 17(5), 1265–1277 (2006)
Learned-Miller, E.G., Fisher III, J.W.: ICA using spacings estimates of entropy. J. Mach. Learn. Res. 4(7-8), 1271–1295 (2004)
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Slapak, A., Yeredor, A. (2012). Charrelation Matrix Based ICA. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_14
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DOI: https://doi.org/10.1007/978-3-642-28551-6_14
Publisher Name: Springer, Berlin, Heidelberg
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