Hybrid Genetic Algorithm (HyGA) and Self – Organizing Maps (SOMs)Kohonen’s Self-Organizing Maps (SOMs) is an unsupervised nonparametric ArtificialNeural Network method (ANN). Where SOMs transform patterns of randomdimensionality into the responses of 2-D arrays of neurons. An important characteristicof the SOMs is the capability to conserves neighborhood relationships of theinput pattern. A distinctive SOMs structure consists of an input and an output layer (Figure 5). The number of input neurons is equal to the dimensions of the input dataand neurons are arranged in a 2-D array where each input is completely connectedto all units. The values of the initial weights are randomly created, and their influencefor the final state decreases as the number of trials increases or decreases 55.SOMs segmentation of a satellite image by mapping patterns from a 3-D into a 2-Dspace. The network size is determined by the image size which can be computedempirically. The network is depicted by a mesh of n n neurons which representscluster units, such that each neuron represents the values of a pixel in three differentbands of the image.During the training phase, the cluster unit is elected as a winnerbased on an input pattern matching the unit weight. This matching is based on theminimum value obtained by using Euclidean distance. (Equation 2). Where v is the input vector, l is the weight of the selected unit l at repetition k, and Wbkci is the weight for neuron i at iteration k. This selected unit and a neighborhoodaround it are then updated. All the neurons within a certain neighborhoodaround the leader participate in the weight update process (Equation 3). This processcan be described by an iterative procedure.Where is a smoothing Kernel which can be written in terms of the followingGaussian function:where T is the total number of iterations defined previouslyto be 1000. Iterations. is the initial guiding rate, and the default value is 0.1.The guiding rate is updated with every cycle as follow. is the search distance at iteration k; initially, can be half the length of thenetwork. As learning proceeds, the size of the neighborhood should be reduced untilit includes only a single unit. The function is described by the following equation.After the SOMs reaches a balanced state, the image is mapped from an unlimitedcolor space to a smaller dimension color space. The number of colors in this spaceis equal to the number of neurons of the SOMs network. The final weight vectors inthe map are used as the new sample space. Each neuron represents the pixels withtheir common gray levels (the final weight multiplied by 255) for each band (threebands). These results are used for clustering, by computing from the weights valuesa set of cluster centers. The results obtained by the segmentation process of the imageusing SOMs is a local optimal one. It is expected that this solution is describedas an over-segmented one where the following guidelines are not respected in thefinal result: i and j, , there is no overlap of the regions. The violation of the aboverules leads to over-segmentation . This is normally an NP problem that is every timethe same algorithm is run with different parameters (iteration numbers, networksize) different solution is obtained. To generate stability in the provided solution bySOMs it is essential to discover a global optimal solution. Usually, GA is an examiningprocess which is built upon the laws of natural selection. Usually, it consistsmainly of selection; genetic operations; and replacement. Genetic operations arecrossover (reproduction ) where two parents are selected to reproduce, and mutationis the process of altering one gene from one kind to another. Finally, replacementis the process of substituting two parents with the newly evolved children. An importantcharacteristic of GA is its capacity to discover the global optimal solutionwithout being stuck in the local minima 56.Sometime the complexity of the imagesegmentation problem makes it difficult to avoid falling in the local optima. To solvethis matter a new procedure is added to GA, this new process is called Hill Climbing. That is why the new technique is called Hybrid GA (HyGA). The Hill Climbingworks by reducing the speed of convergence by penalizing individuals in the population(reducing fitness of the fittest). The segmentation procedure of the new method(Figure 6) starts by reading a satellite image. Then SOMs uses the image featuresto combine the pixels into groups. The cluster center of each group is provided to