# Essay about A Proposed ICA Algorithm

1443 Words6 Pages
Proposed ICA algorithm This algorithm performs adaptive optimization of kurtosis based contrast function in floating point arithmetic. The main aim of this algorithm development is to reduce the number of manipulations and to improve the performance of ICA algorithm in terms of convergence speed, area, frequency and power. The convergence speed of the algorithm is improved by focusing the search in particular directions rather than searching for the solution in a random manner. The random number generator unit present in FastICA has been replaced by an adaptive optimization unit .This adaptive optimization unit updates the weight values based on the kurtosis function. Since adaptive optimization unit contains a subtractor and…show more content…
If x is normalized so variance is equal to unity, then kurtosis is simply the normalized version of the fourth moment as in (5). kurt(x)=E{x^(4 ) }-3 (5) Kurtosis value is non-zero for non-gaussian random variables or signals. The weight vector is updated in ICA by the learning rule w_newi (k+1)←E{Z.g(〖w(k)Z〗^T)}-E{Z.g'(〖w(k)Z〗^T)} (6) Where g( ) is a nonlinear function. Since derivative of kurtosis can be used as a nonlinear function g(x)=x3 (7) On substituting (7) in (6), w_newi (k+1)←E{Z.(〖w(k)Z〗^T)}-3E{Z〖〖(w(k)Z〗^T)〗^2} (8) Due to the property of unit variance, the equation (8) becomes, w_newi (k+1)←E{Z.(〖w(k)Z〗^T)}-3w(k) (9) This is used in main iteration of proposed algorithm for weight updation.The Fig 2 shows the architecture of iteration process defined in (9) for 2 sources . Prposed ICA Algorithm for 2 units Having the low dimensionality signal obtained from preprocessing step, this algorithm aims at finding the vectors of demixing matrix to extract desired signal from the mixtures. Updation of weights continues in iterative manner with following steps until a convergence is achieved. The proposed ICA algorithm estimates one column of the demixing matrix in one convergence period. Form a weight matrix W by assuming M sub matrices or column vectors where M