Abstract
We present a new method, that is able to separate one or a few particular sources from a linear mixture, performing source separation and dimensionality reduction simultaneously. This is in particular useful in situations in which the number of observations is much larger than the number of underlaying sources, as it allows to drastically reduce the number of the parameters to estimate. It is well applicable for the long time series recorded in optical imaging experiments. Here one is basically interested in only one source containing the stimulus response. The algorithm is based on the technique of joint diagonalization of cross correlation matrices. To focus the convergence to the desired source, prior knowledge is incorporated. It can be derived, for instance, from the expected time course of the metabolic response in an optical imaging experiment. We demonstrate the capabilities of this algorithm on the basis of toy data coming from prototype signals of former optical recording experiments and with time courses that are similar to those obtained in optical recording experiments.
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References
Anthony J. Bell and Terrence J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Computation, vol. 7, no. 6, pp. 1129–1159, 1995.
A. Hyvärinen and E. Oja, “A fast fixed point algorithm for independent component analysis.,” Neural Comput., vol. 9, pp. 1483–1492, 1997.
G.G. Blasdel and G. Salama, “Voltage-sensitive dyes reveal a modular organization in monkey striate cortex.,” Nature, vol. 321, pp. 579–585, 1986.
H. Schöner, M. Stetter, I. Schieβl, J. Mayhew, J. Lund, N. McLoughlin, and K. Obermayer, “Application of blind separation of sources to optical recording of brain activity,” in Advances in Neural Information Processing Systems NIPS 12, S.A. Solla, T.K. Leen, and K.-R. Müller, Eds. 2000, pp. 949–955, MIT Press, In press.
A. Belouchrani, K. Abed-Meraim, J. Cardoso, and E. Moulines, “A blind source separation technique using second-order statistics,” IEEE transactions on Signal Processing, no. 45, pp. 434–444, 1997.
L. Molgedey and H. G. Schuster, “Separation of a mixture of independent signals using time delayed correlations,” Phys. Rev. Lett., vol. 72, pp. 3634–3637, 1994.
R. Vollgraf, M. Stetter, and K. Obermayer, “Convolutive decorrelation procedures for blind source separation,” in Proceedings of the 2. International Workshop on ICA, Helsinki, P. Pajunen and J. Karhunen, Eds., 2000, pp. 515–520.
I. Schieβl, H. Schöner, M. Stetter, and K. Obermayer, “Regularized second order source separation,” in Proceedings of the 2. International Workshop on ICA, Helsinki, P. Pajunen and J. Karhunen, Eds., 2000, pp. 111–116.
D. Malonek and A. Grinvald, “Interactions between electrical activity and cortical micro circulation revealed by imaging spectroscopy: implications for functional brain mapping.,” Science, vol. 272, pp. 551–554, 1996.
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Vollgraf, R., Schieβl, I., Obermayer, K. (2001). Blind Source Separation of Single Components from Linear Mixtures. In: Dorffner, G., Bischof, H., Hornik, K. (eds) Artificial Neural Networks — ICANN 2001. ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44668-0_71
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DOI: https://doi.org/10.1007/3-540-44668-0_71
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