Neural network neuron

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Figure 8-1J. Training ofa Kohonen neural network with a chirality code, The number of weights in a neuron is the same as the number of elements in the chirality code vector, When a chirality code is presented to the network, the neuron with the most similar weights to the chirality code is excited (this is the ivinning or central neuron) (see Section 9.5,3),...

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. 

Neural networks model the functionality of the brain. They learn from examples, whereby the weights of the neurons are adapted on the basis of training data. 

Figure 10.2-9. Application of a counterpropagation neural network as a look-up table for IR spectra sinnulation, The winning neuron which contains the RDF code in the upper layer of the network points to the simulated IR spectrum in the lower layer.

Artificial Neural Networks (ANNs) attempt to emulate their biological counterparts. McCulloch and Pitts (1943) proposed a simple model of a neuron, and Hebb (1949) described a technique which became known as Hebbian learning. Rosenblatt (1961), devised a single layer of neurons, called a Perceptron, that was used for optical pattern recognition. 

An ANN is a network of single neurons jointed together by synaptie eonneetions. Figure 10.22 shows a three-layer feedforward neural network. 

A sigmoid (s-shaped) is a continuous function that has a derivative at all points and is a monotonically increasing function. Here 5,p is the transformed output asymptotic to 0 < 5/,p I and w,.p is the summed total of the inputs (- 00 < Ui p < -I- 00) for pattern p. Hence, when the neural network is presented with a set of input data, each neuron sums up all the inputs modified by the corresponding connection weights and applies the transfer function to the summed total. This process is repeated until the network outputs are obtained. 

Neural networks can be broadly classified based on their network architecture as feed-forward and feed-back networks, as shown in Fig. 3. In brief, if a neuron s output is never dependent on the output of the subsequent neurons, the network is said to be feed forward. Input signals go only one way, and the outputs are dependent on only the signals coming in from other neurons. Thus, there are no loops in the system. When dealing with the various types of ANNs, two primary aspects, namely, the architecture and the types of computations to be per-... 

Neural networks can also be classified by their neuron transfer function, which typically are either linear or nonlinear models. The earliest models used linear transfer functions wherein the output values were continuous. Linear functions are not very useful for many applications because most problems are too complex to be manipulated by simple multiplication. In a nonlinear model, the output of the neuron is a nonlinear function of the sum of the inputs. The output of a nonlinear neuron can have a very complicated relationship with the activation value. 

In neural network design, the above parameters have no precise number/answers because it is dependent on the particular application. However, the question is worth addressing. In general, the more patterns and the fewer hidden neurons to be used, the better the network. It should be realized that there is a subtle relationship between the number of patterns and the number of hidden layer neurons. Having too few patterns or too many hidden neurons can cause the network to memorize. When memorization occurs, the network would perform well during training, but tests poorly with a new data set. 

The specific volumes of all the nine siloxanes were predicted as a function of temperature and the number of monofunctional units, M, and difunctional units, D. A simple 3-4-1 neural network architecture with just one hidden layer was used. The three input nodes were for the number of M groups, the number of D groups, and the temperature. The hidden layer had four neurons. The predicted variable was the specific volumes of the silox-... 

Figure 6 Schematic of a typical neural network training process. I-input layer H-hidden layer 0-output layer B-bias neuron.

Kolmogorov s Theorem (Reformulated by Hecht-Nielson) Any real-valued continuous function f defined on an N-dimensional cube can be implemented by a three layered neural network consisting of 2N -)-1 neurons in the hidden layer with transfer functions from the input to the hidden layer and (f> from all of... 

The basic component of the neural network is the neuron, a simple mathematical processing unit that takes one or more inputs and produces an output. For each neuron, every input has an associated weight that defines its relative importance, and the neuron simply computes the weighted sum of all the outputs and calculates an output. This is then modified by means of a transformation function (sometimes called a transfer or activation function) before being forwarded to another neuron. This simple processing unit is known as a perceptron, a feed-forward system in which the transfer of data is in the forward direction, from inputs to outputs, only. 

A neural network consists of many neurons organized into a structure called the network architecture. Although there are many possible network architectures, one of the most popular and successful is the multilayer perceptron (MLP) network. This consists of identical neurons all interconnected and organized in layers, with those in one layer connected to those in the next layer so that the outputs in one layer become the inputs in the subsequent... 

Aqueous solubility is selected to demonstrate the E-state application in QSPR studies. Huuskonen et al. modeled the aqueous solubihty of 734 diverse organic compounds with multiple linear regression (MLR) and artificial neural network (ANN) approaches [27]. The set of structural descriptors comprised 31 E-state atomic indices, and three indicator variables for pyridine, ahphatic hydrocarbons and aromatic hydrocarbons, respectively. The dataset of734 chemicals was divided into a training set ( =675), a vahdation set (n=38) and a test set (n=21). A comparison of the MLR results (training, r =0.94, s=0.58 vahdation r =0.84, s=0.67 test, r =0.80, s=0.87) and the ANN results (training, r =0.96, s=0.51 vahdation r =0.85, s=0.62 tesL r =0.84, s=0.75) indicates a smah improvement for the neural network model with five hidden neurons. These QSPR models may be used for a fast and rehable computahon of the aqueous solubihty for diverse orgarhc compounds. 

A more recently introduced technique, at least in the field of chemometrics, is the use of neural networks. The methodology will be described in detail in Chapter 44. In this chapter, we will only give a short and very introductory description to be able to contrast the technique with the others described earlier. A typical artificial neuron is shown in Fig. 33.19. The isolated neuron of this figure performs a two-stage process to transform a set of inputs in a response or output. In a pattern recognition context, these inputs would be the values for the variables (in this example, limited to only 2, X and x- and the response would be a class variable, for instance y = 1 for class K and y = 0 for class L. 

The structural unit of artificial neural networks is the neuron, an abstraction of the biological neuron a typical biological neuron is shown in Fig. 44.1. Biological neurons consist of a cell body from which many branches (dendrites and axon) grow in various directions. Impulses (external or from other neurons) are received through the dendrites. In the cell body, these signals are sifted and integrated. 

Each set of mathematical operations in a neural network is called a layer, and the mathematical operations in each layer are called neurons. A simple layer neural network might take an unknown spectrum and pass it through a two-layer network where the first layer, called a hidden layer, computes a basis function from the distances of the unknown to each reference signature spectrum, and the second layer, called an output layer, that combines the basis functions into a final score for the unknown sample. 

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