Artificial neurons function

The nervous systems and especially the brains of animals and humans work very fast, efficiently, and highly in parallel. They consist of networked neurons which work together and interchange signals with one another. This section describes the functionality of a biological neuron and explains the model of an artificial neuron. 

Artificial Neural Networks (ANNs) are information processing imits which process information in a way that is motivated by the functionality of the biological nervous system. Just as the brain consists of neurons which are connected with one another, an ANN comprises interrelated artificial neurons. The neurons work together to solve a given problem. 

Figure 9-13. Artificial neuron the signals x, are weighted (with weights IV,) and summed to produce a net signal Net. This net signal is then modified by a transfer function and sent as an output to other neurons,...

The basic model of a single artificial neuron consists of a weighted summer and an activation (or transfer) function as shown in Figure 10.20. Figure 10.20 shows a neuron in the yth layer, where... 

Fig. 44.2. An artificial neuron x,. ..Xp are the incoming signals wi... Wp are the corresponding weight factors and F is the transfer function.

A biological neuron can be active (excited) or inactive (not excited). Similarly, the artificial neurons can also have different activation status. Some neurons can be programmed to have only two states (active/inactive) as the biological ones, but others can take any value within a certain range. The final output or response of a neuron (let us call it a) is determined by its transfer function, f, which operates on the net signal (Netj) received by the neuron. Hence the overall output of a neuron can be summarised as ... 

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. 

Chemometrics is a branch of science and technology dealing with the extraction of useful information from multidimensional measurement data using statistics and mathematics. It is applied in numerous scientific disciplines, including the analysis of food [313-315]. The most common techniques applied to multidimensional analysis include principal components analysis (PCA), factor analysis (FA), linear discriminant analysis (LDA), canonical discriminant function analysis (DA), cluster analysis (CA) and artificial neurone networks (ANN). 

The algorithm of an ANN imitates the information processing in the human brain, whose capabilities in image processing are undefeated so far. The self-organizing map consists of artificial neurons that are characterized by weight vectors with the same dimensionality as the descriptor set The artificial neurons are connected by a distance-dependent function. 

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. 

An artificial neural network (ANN), usually called neural network (NN), is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes information using a connectionist... 

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). 

The 0 is a threshold value that a neuron must receive to be activated. Biologically, this happens inside the cell but the artificial neuron needs a dedicated function (equation). This threshold value (and its related mathematical function) is called bias. 

The artificial neural network (ANN) is a system imitating the operation of a biological neural network. It is composed of the set of basic elements (artificial neurons) that are mutually connected. In general, to describe the ANN operation at least three basic properties should be known namely a neuron model (transfer function), the network topology and the method of training. 

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.)...

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