Abstract
In this paper, a new objective function of ICA is proposed by a probabilistic approach to the quadratic terms. Many previous ICA methods are sensitive to the sign of kurtosis of source (sub- or super-Gaussian), where the change of the sign often causes a large discontinuity in the objective function. On the other hand, some other previous methods use continuous objective functions by using the squares of the 4th-order statistics. However, such squared statistics often lack the robustness because they magnify the outliers. In this paper, we solve this problem by introducing a new objective function which is given as a summation of weighted 4th-order statistics, where the kurtoses of sources are incorporated “smoothly” into the weights. Consequently, the function is always continuously differentiable with respect to both the kurtoses and the separating matrix to be estimated. In addition, we propose a new ICA method optimizing the objective function by the Givens rotations under the orthonormality constraint. Experimental results show that the proposed method is comparable to the other ICA methods and it outperforms them especially when sub-Gaussian sources are dominant.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Amari, S., Cichocki, A.: A new learning algorithm for blind signal separation. In: Touretzky, D., Mozer, M., Hasselmo, M. (eds.) Advances in Neural Information Processing Systems, vol. 8, pp. 757–763. MIT Press, Cambridge (1996)
Cardoso, J.F.: High-order contrasts for independent component analysis. Neural Comput. 11(1), 157–192 (1999)
Cardoso, J.F., Souloumiac, A.: Blind beamforming for non Gaussian signals. IEE Proceedings-F 140(6), 362–370 (1993)
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. Wiley, New York (2002)
Comon, P.: Independent component analysis - a new concept? Signal Process. 36, 287–314 (1994)
Delorme, A., Makeig, S.: EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J. Neurosci. Methods 134(1), 9–21 (2004)
Hyvärinen, A.: Blind source separation by nonstationarity of variance: a cumulant-based approach. IEEE Trans. Neural Netw. 12(6), 1471–1474 (2001)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001)
Lee, T.W., Girolami, M., Sejnowski, T.J.: Independent component analysis using an extended infomax algorithm for mixed subgaussian and supergaussian sources. Neural Comput. 11(2), 417–441 (1999)
Matsuda, Y., Yamaguchi, K.: An adaptive threshold in joint approximate diagonalization by assuming exponentially distributed errors. Neurocomputing 74, 1994–2001 (2011)
Matsuda, Y., Yamaguchi, K.: A robust objective function of joint approximate diagonalization. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds.) ICANN 2012, Part II. LNCS, vol. 7553, pp. 205–212. Springer, Heidelberg (2012)
Matsuda, Y., Yamaguchi, K.: Ensemble joint approximate diagonalization by an information theoretic approach. In: Lee, M., Hirose, A., Hou, Z.-G., Kil, R.M. (eds.) ICONIP 2013, Part III. LNCS, vol. 8228, pp. 309–316. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Matsuda, Y., Yamaguchi, K. (2015). Objective Function of ICA with Smooth Estimation of Kurtosis. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9491. Springer, Cham. https://doi.org/10.1007/978-3-319-26555-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-26555-1_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26554-4
Online ISBN: 978-3-319-26555-1
eBook Packages: Computer ScienceComputer Science (R0)