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Unsupervised Learning While plenty of work has been done in using PSO algorithms to train supervised networks, not much has been done to show how PSO performs as an unsupervised training algorithm Xiao et al [921] used the gbest PSO to evolve weights for a selforganizing map (SOM) [476] (also refer to Section 45) to perform gene clustering The training process consists of two phases The rst phase uses PSO to nd an initial weight set for the SOM The second phase initializes a PSO with the weight set obtained from the rst phase The PSO is then used to re ne this weight set

Of the amounts listed on the remittance advice, the medical insurance and 401k deductions are voluntary, and so cannot be included in the calculation of disposable earnings This increases Mr Evans s disposable earnings to $625 The payroll manager then multiplies this amount by 60 percent, which is the maximum amount of disposable earnings that can be remitted for child support The result is $375, $15 less than the $390 listed on the court order The payroll manager begins deducting and remitting the $375 per week

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Messerschmidt and Engelbrecht [580], and Franken and Engelbrecht [283, 284, 285] used the gbest, lbest and Von Neumann PSO algorithms as well as the GCPSO to coevolve neural networks to approximate the evaluation function of leaf nodes in game trees No target values were available; therefore NNs compete in game tournaments against groups of opponents in order to determine a score or tness for each NN During the coevolutionary training process, weights are adjusted using PSO algorithms to have NNs (particles) move towards the best game player The coevolutionary training process has been applied successfully to the games of tick-tack-toe, checkers, bao, the iterated prisoner s dilemma, and a probabilistic version of tick-tack-toe For more information, refer to Section 1523

Zhang and Shao [949, 950] proposed a PSO model to simultaneously optimize NN weights and architecture Two swarms are maintained: one swarm optimizes the architecture, and the other optimizes weights Particles in the architecture swarm are two-dimensional, with each particle representing the number of hidden units used and the connection density The rst step of the algorithm randomly initializes these architecture particles within prede ned ranges The second swarm s particles represent actual weight vectors For each architecture particle, a swarm of particles is created by randomly initializing weights to correspond with the number of hidden units and the connection density speci ed by the architecture particle Each of these swarms is evolved using a PSO, where the tness function is the MSE computed from the training set After convergence of each NN weights swarm, the best weight vector is identi ed from each swarm (note that the selected weight vectors are of di erent architectures) The tness of these NNs are then evaluated using a validation set containing patterns not used for training The obtained tness values are used to quantify the performance of the di erent architecture speci cations given by the corresponding particles of the architecture swarm Using these tness values, the architecture swarm is further optimized using PSO This process continues until a termination criterion is satis ed, at which point the global best particle is one with an optimized architecture and weight values

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