Robust Independent Component Analysis via Time-Delayed Cumulant Functions
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概要
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In this paper we consider blind source separation (BSS) problem of signals which are spatially uncorrelaled of order four, but temporally correlated of order four (for instance speech or biomedical signals). For such type of signals we propose a new sufficient condition for separation using fourth order statistics, stating that the separation is possible, if the source signals have distinct normalized cumulant functions (depending on time delay). Using this condition we show that the BSS problem can be converted to a symmetric eigenvalue problem of a generalized cumulant matrix Z^<(4)>(b) dependingon L-dimensional parameterb, if this matrix has distinct eigenvalues. We prove that the set of parameters b which produce Zl^<(4)>(b) with distinct eigenvalues form an open subset of IR^L, whose complement has a measure zero. We propose a new separating algorithm which uses Jacobi's method for joint diagonalization of cumulant matrices depending on time delay. We empasize the following two features of this algorithm : 1) The optimal number of matrices for joint diago- nalization is 100 150 (established experimentally), which for large dimensional problems is much smaller than those of JADE ; 2) It works well even if the signals from the above class are, additionally, white (of order two) with zero kurtosis (as shown by an example).
- 一般社団法人電子情報通信学会の論文
- 2003-03-01
著者
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GEORGIEV Pando
Lab.for Advanced Brain Signal Processing,Brain Science Institute,RIKEN
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Georgiev Pando
Lab.for Advanced Brain Signal Processing. Brain Science Institute Riken
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CICHOCKI Aadrzej
Lab.for Advanced Brain Signal Processing. Brain Science Institute,RIKEN
関連論文
- Blind Source Separation Algorithms with Matrix Constraints
- Robust Independent Component Analysis via Time-Delayed Cumulant Functions