In the second stage, supervised optimization procedures sellekchem are involved in the optimal estimation of the connecting weights.One effective clustering approach for finding centers is the K-means algorithm [2]. However, because of iterative crisp clustering operations, the results of the K-means algorithm are sensitive to the selection of initial centers. In addition, the computation complexities of the algorithm are high for large set of training vectors. The fuzzy C-means (FCM) algorithm and its variants [3,4] are the effective alternatives for finding the centers. The Inhibitors,Modulators,Libraries FCM adopts a fuzzy partitioning approach for clustering. It allows the training vectors to belong to several clusters simultaneously, with Inhibitors,Modulators,Libraries different degrees of membership.

Although the FCM is also an iterative algorithm, the clustering Inhibitors,Modulators,Libraries performance is less susceptible to the initial centers. However, the fuzzy clustering involves the computation of degree of membership, which may be very computationally expensive as the number of training vectors and/or the number of clusters become large. The particle swarm optimization (PSO) techniques [5,6] are also beneficial for computing the centers. The techniques can operate in conjunction with fuzzy clustering [6] for attaining near optimal performance. Nevertheless, when the number of particles and/or the dimension associated with each particle are large, the real-time RBF training may still be difficult.To estimate the connecting weights in the output layer, least mean square (LMS) methods are the commonly used techniques.

However, basic LMS approach involves the computation of the inverse of the correlation matrix in the hidden layer of the RBF Inhibitors,Modulators,Libraries network. When the size of the hidden layer and/or training set becomes large, the inverse matrix computation may become a demanding task. The requirement of inverse matrix operations can be lifted by the adoption of recursive LMS. Nevertheless, because extensive matrix multiplications are required, especially for large hidden layer and/or training set, the recursive LMS still has high computational complexities.Many efforts have been made to expedite RBF training. The techniques in [7�C9] focus on reducing the training time for centers. The algorithm presented in [7] uses subtractive clustering. The fast technique in [8] modifies the basic K-means algorithm. The center updating in [9] is based on an incremental scheme.

In [10], an incremental technique is used for the updating of connecting weights in the output layer. These fast algorithms Batimastat are implemented by software. despite Therefore, only moderate acceleration can be achieved. Moreover, for the incremental algorithms [9,10], inappropriate selection of learning rate may severely degrade the training performance.The algorithm in [11] is suited for finding centers by hardware. It involves only replicating selected training vectors as centers. The number of centers produced by the algorithm can be controlled by the radius parameter [11].