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Graph of the Logistic function and its derivative function. 

Graph of the Logistic function and its derivative function. 

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Among numerous artificial intelligence approaches, k-Nearest Neighbor algorithms, genetic algorithms, and artificial neural networks are considered as the most common and effective methods in classification problems in numerous studies. In the present study, the results of the implementation of a novel hybrid feature selection-classification model...

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... of this genetic algorithm that evaluates the members of population can be the k-NN classifier. Thus, the k-NN method performs the classification based on feature arrays. The efficiency of the k-NN approach for each of the arrays determines the array’s fitness. Next, weighted random selection is performed on the members of the population using the Roulette wheel approach. The value of these weights is determined based on the results obtained from the fitness function. Now, crossover operator is performed on each pair of the feature array that was selected as parents to produce the children of the new generation. In this study, the one- point crossover method was used from among various crossover methods. That is in each pair of features’ array selected as parents from a randomly selected point, part of the two arrays are exchanged with each other. If there is a specific feature in two arrays of features selected for crossover, it is possible that, due to crossover, the children of the new generation contain repetitive features. The mutation operator (that randomly replaces a specific feature with a value within its permissible limit) is used as a solution for solving this problem. By performing these steps, the first repetition of algorithm is finished, and a new generation with combination of children and members of the initial population, which had a higher fitness, is created. By utilization this generation as the next repetitive primary population, the algorithmic steps continues until reaching the stop condition. At the end of the genetic algorithm steps, the process of reducing and selecting the features does, in effect, finish, and the obtained results are the best feature arrays that could assist the classification in the next step. Step 5. Classifying new instance vector X ’ using modification k-NN The classification is implemented using the k-NN method with a modification in its algorithm, that is in the final decision making step of determining class label of the new instance. For classification of every new instance vector X ’ , similar to conventional k-NN method, first it calculates the distance (usually Euclidean) of this instance to all the other instances of the training set (whose class label is known). Second, these calculated distances are sorted. Then, k of the closest instances/neighbors of the training set to the new instance is selected. In conventional k-NN, the final decision about determining the class label of the new instance vector is made based on the majority vote of these k closest neighbors. While in the present study, this step of the k-NN improved by the allocation of Fuzzy class membership to the new instance/input vector (i.e., incorporating Fuzzy set theory (Fuzzy Logic) instead of crisp set theory (Boolean Logic) in k- NN). That is, an array with a dimension equal to the number of classes is built (i.e., ‘‘Fuzzy class membership array’’), the votes of every of classes is inserted into the array (without exertion of the majority of votes). In effect, the Fuzzy class membership arrays is calculated through equation 1: where k is the number of nearest neighbors and Xj, is j the nearest neighbor of X ’ in the k-NN method and d ( c i , c ( X j ) is the indicator function. Hence, this array is indicative of the degree of belongingness of the new instance X ’ to each class (i.e., the results of dividing the number of neighbors belonging to each of the classes by the number of k). In this stage, the class membership array is calculated for each of the output feature’s arrays of GA. Subsequently (in steps 8 and 9), these arrays along with the Fuzzy class membership array derived from DBPNN are integrated together to predict final class label of this new instance X ’ . Step 6. Introducing Dynamic BackPropagation Neural Network The main aim of this phase is the introduction of a newly improved neural network that advances the classification process in parallel with the k-NN method that was improved in the previous step. It is expected that, with regard to the different construct of these two classification approaches, the classification be improved using the high potential resulting from the synergy between the elements of these two classification approaches. In effect, the presented model is a dynamic neural network that in this study is called the DBPNN. The difference of the new method with the traditional BPNN method is that in each epoch, the transfer function is made dynamic in a way that the learning speed and accuracy is increased remarkably. Usually, functions such as log-Sigmoid (logistic) and/or tan-Sigmoid are the most common transfer functions used in BPNNs. These functions, owing to their desirable characteristics, have shown an appropriate performance in feedback neural networks. One of their benefits is that derivative of these functions is obtained according to the function, that is (Equations 2–3): The graph and the derivative of this function are shown in Figure 3. To increase the speed and the learning accuracy, the active domain is made dynamic in this study. In logistic function, the domain is ( 2‘ ‘ ) and the range is [0 1], but its active domain is limited to the range [ 2 4, 4]. In other words, this function takes the value around zero for the values of range ( 2‘ 2 4), and a number around 1 for the values of range (4 ‘ ) (with a maximum level of error of 0.018; that is the output equals to 0 or 1, ignoring this error). In the new method, DBPNN, there is an attempt to modify sigmoid function parameters in each epoch in a way that the active domain correspond to network inputs and weights. Therefore, we try to achieve this goal, step by step, by the application of suitable modifications. As mentioned above, the range of the Sigmoid logarithm function is the interval [0 1]. Now, we intend to define a function with Sigmoid logarithm nucleus whose range interval is [ 2 1 1]. To this end, we must define a map from [0 1] to [ 2 1 1]. Assuming that this map is a linear modifier, we can consider y ~ 2x { 1 , and consequently we have equations ...

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