Characteristic-function-based independent component analysis

A novel characteristic-function-based method for blind separation of statistically independent source signals is proposed in the independent component analysis (ICA) framework. The definition of independence may be given in terms of factorization of joint characteristic function. Three criteria for ICA are derived based on this property. These criteria always exist and two of them have desirable large sample properties. An objective function for estimating the independence criteria directly from data is proposed. An efficient algorithm using Fourier coefficients is developed for minimizing the objective function. Simulation results demonstrate that the method performs reliably even in such situations where many widely used ICA methods may fail.

[1]  Petr Tichavsky,et al.  Independent Component Analysis through Direct Estimation of the Mutual Information , 2000 .

[2]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[3]  E. Oja,et al.  Independent Component Analysis , 2013 .

[4]  A. Kankainen,et al.  A consistent modification of a test for independence based on the empirical characteristic function , 1998 .

[5]  Roger Cuppens,et al.  Decomposition of multivariate probabilities , 1975 .

[6]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[7]  Jean-Franois Cardoso.  High-Order Contrasts for Independent Component Analysis , 1999, Neural Computation.

[8]  A. Feuerverger,et al.  A Consistent Test for Bivariate Dependence , 1993 .

[9]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[10]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[11]  S. Csörgo.  Multivariate empirical characteristic functions , 1981 .

[12]  Eric Moreau,et al.  A generalization of joint-diagonalization criteria for source separation , 2001, IEEE Trans. Signal Process..

[13]  Ruey-Wen Liu,et al.  General approach to blind source separation , 1996, IEEE Trans. Signal Process..

[14]  Jean-Christophe Pesquet,et al.  Cumulant-based independence measures for linear mixtures , 2001, IEEE Trans. Inf. Theory.

[15]  Jan Eriksson,et al.  Novel Characteristic Function Based Criteria For Ica , 2001 .

[16]  Visa Koivunen,et al.  Adaptive Score Functions for Maximum Likelihood ICA , 2002, J. VLSI Signal Process..

[17]  A. J. Bell,et al.  A Unifying Information-Theoretic Framework for Independent Component Analysis , 2000 .

[18]  Eugene Lukacs,et al.  Developments in Characteristic Function Theory , 1976 .

[19]  Joos Vandewalle,et al.  Independent component analysis and (simultaneous) third-order tensor diagonalization , 2001, IEEE Trans. Signal Process..

[20]  Arie Yeredor,et al.  Blind source separation via the second characteristic function , 2000, Signal Process..

[21]  Andrzej Cichocki,et al.  Flexible Independent Component Analysis , 2000, J. VLSI Signal Process..

[22]  Jean-Francois Cardoso,et al.  Blind signal separation: statistical principles , 1998, Proc. IEEE.

[23]  Visa Koivunen,et al.  Blind Separation Using Characteristic Function Based Criterion , 2001 .

[24]  V. Koivunen,et al.  Identifiability and Separability of Linear Ica Models Revisited , 2003 .

[25]  I︠u︡. V. Linnik,et al.  Decomposition of Random Variables and Vectors , 1977 .