In the one-unit approach, the ith extracting vector wi can be orthogonal to the space spanned by the vector w1, w2, ��, wi-1, by Gram-Schmidt method, that is wi=wi-��j=1i-1(wjHwi)wj.In the symmetric algorithm the symmetric orthogonalization Wortmannin clinical trial procedure can be approximately finished by (WWH)?1/2W. Therefore, the one-unit and symmetric version of the proposed algorithm with spatial constraint are summarized in Algorithms 1 and 2 respectively. We refer them to as Alg 1 and Alg 2 in the later analysis for simplicity.Algorithm 1. The one-unit extracting algorithm with spatial constraint.
InitializationWhitened the observation data x to give Z = Vx;forP = 1, ��,lSet ��(0), ��1, ��2 and choose a random initial weight vector w(0) with unity normIterationAt the ith iteration for obtaining Inhibitors,Modulators,Libraries Wp,Calculate ��w�� according to Equation (19) by utilizing Wp(i?1) respectivelywp(i)��wp(i-1)+��1?w��(wp(i-1))wp(i)��wp(i)-��j=1p-1wjHwp(i)wjwp(i)��wp(i)/��wp(i)����(i)����(i-1)-��2max(J2(wp(i)),0)TerminationThe Inhibitors,Modulators,Libraries iteration is terminated when the relative change ��wp(i)-wp(i?1)�� is less than a specified tolerance.end forAlgorithm 2. The symmetric extracting algorithm with spatial constraint.InitializationWhitened the observation data x to give z = Vx;Set ��(0), ��1, ��2 and choose a random initial weight matrix W(0) = |w1(0), ��, wl(0)|with wl(0) having unity normIterationAt the ith iteration for obtaining W,forP = 1, ��, lCalculate w�� Inhibitors,Modulators,Libraries according to Equation (19) by utilizing wp(i-1) respectivelywp(i)��wp(i-1)+��1?w��(wp(i-1))end forw(i)��(w(i)(w(i))H)-1/2w(i)��(i)����(i-1)-��2max(min(J2(wp(i))),0)p=1,?,lTerminationThe iteration is terminated when the relative change ��W(i) ? W(i?1)�� less than a specified tolerance.
Yet Alg1 and Alg2 require a user parameter which may affect the final results significantly. The selection of the threshold in the algorithm is of vital importance for extracting the desired signal successfully, which can Inhibitors,Modulators,Libraries be found in Section 5 by simulation. Furthermore, the update step of the Lagrangian parameter in each iteration will GSK-3 increase the computational load of the algorithm. Therefore, it is important to develop user parameters free methods.4.2. A Novel MethodIf the number of source signals is N, there will be 2N local maxima of negentropy, each one of which corresponds to ��si(n).
The FastICA algorithm cannot theoretically obtain particular desired independent sources other than those having the maximum negentropy selleck products among the sources. Furthermore, as we know, the FastICA algorithm is a local optimization algorithm which may arbitrarily converge to different local maxima from time to time because the local convergence depends on a number of factors such as the initial weight vector and the learning rate. When one desires a specific solution, the FastICA algorithm is of little use, unless the ��interesting�� independent source lies in the neighborhood of the initialization.