Artificial neurons input function

Table 5.1 Activation functions currently employed in artificial neurons, where n represents the overall net input to the neuron and a denotes the result of the activation function...

Our choice for the non-linear system approach to PARC is the ANN. The ANN is composed of many neurons configured in layers such that data pass from an input layer through any number of middle layers and finally exit the system through a final layer called the output layer. In Fig. 4 is shown a diagram of a simple three-layer ANN. The input layer is composed of numeric scalar data values, whereas the middle and output layers are composed of artificial neurons. These artificial neurons are essentially weighted transfer functions that convert their inputs into a single desired output. The individual layer components are referred to as nodes. Every input node is connected to every middle node, and every middle node is connected to every output node. 

FIGURE 4.10 Schematic image of an artificial neuron. The input data x are calculated with their connective weight w to form the Net value of the neuron. A transfer function is applied to mimic the threshold of the biological neuron. The out value represents the outcome of the process, which is fed to another artificial neuron. 

Neural network has been widely used in fields of function approximation, pattern recognition, image dealing, artificial intelligence, optimization and so on [26, 102]. Multilayer feed forward artificial neural network is a major type of the neural network which is connected by input layer, one or more output layers and hidden layers in a forward way. Each layer is composed of many artificial neurons. The output of previous layer neurons is the input of the next layer as shown in Fig. 2.6. 

Fig. 1 Scheme of an artificial neuron. First, several input numbers x, are added. Then a function/ is applied to this sum to yield the output y. 

The ANNs were developed in an attempt to imitate, mathematically, the characteristics of the biological neurons. They are composed by intercoimected artificial neurons responsible for the processing of input-output relationships, these relationships are learned by training the ANN with a set of irqmt-output patterns. The ANNs can be used for different proposes approximation of functions and classification are examples of such applications. The most common types of ANNs used for classification are the feedforward neural networks (FNNs) and the radial basis function (RBF) networks. Probabilistic neural networks (PNNs) are a kind of RBFs that uses a Bayesian decision strategy (Dehghani et al., 2006). 

Figure 9.6. Artificial neuron or node, p, a, and w represent the input, output, and weight, respectively. n is the net input and/is the transfer function. (Reproduced from [26], by permission of John Wiley Sons, Ltd. copyright 2002.)...

The solution of the exact interpolating RBF mapping passes through every data point (x , y ). In the presence of noise, the exact solution of the interpolation problem is typically a function oscillating between the given data points. An additional problem with the exact interpolation procedure is that the number of basis functions is equal to the number of data points, so calculating the inverse of the N x N matrix becomes intractable in practice. The interpretation of the RBF method as an artificial neural network consists of three layers a layer of input neurons feeding the feature vectors into the network a hidden layer of RBF... 

Artificial neural networks (Hurtado 2004) are computational devices which permit the approximate calculation of outputs given an input set. The input is organized as a layer of neurons, each corresponding to one of the input variables, and the output is contained in an output layer. Intermediate, hidden layers, contain a number of neurons which receive information from the input layer and pass it on to subsequent layers. Each link in the network is associated with a weight w. The total information received by a neuron is processed by a transfer function h before being sent forward to the neurons in the next layer. For a network with a single hidden layer, the computational process can be expressed as... 

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