Artificial neural networks hidden layers

Figure 9-16. ArtiFicial neural network architecture with a two-layer design, compri ing Input units, a so-called hidden layer, and an output layer. The squares Inclosing the ones depict the bias which Is an extra weight (see Ref, [10 for further details),...

Artificial neural networks (ANN) are computing tools made up of simple, interconnected processing elements called neurons. The neurons are arranged in layers. The feed-forward network consists of an input layer, one or more hidden layers, and an output layer. ANNs are known to be well suited for assimilating knowledge about complex processes if they are properly subjected to input-output patterns about the process. 

An artificial neural network (ANN) model was developed to predict the structure of the mesoporous materials based on the composition of their synthesis mixtures. The predictive ability of the networks was tested through comparison of the mesophase structures predicted by the model and those actually determined by XRD. Among the various ANN models available, three-layer feed-forward neural networks with one hidden layer are known to be universal approximators [11, 12]. The neural network retained in this work is described by the following set of equations that correlate the network output S (currently, the structure of the material) to the input variables U, which represent here the normalized composition of the synthesis mixture ... 

Figure 8.2 A motor neuron (a) and small artificial neural network (b). A neuron collects signals from other neurons via its dendrites. If the neuron is sufficiently activated, it sends a signal to other neurons via its axon. Artificial neural network are often grouped into layers. Data is entered through the input layer. It is processed by the neurons of the hidden layer and then fed to the neurons of the output layer. (Illustration of motor neuron from Life ART Collection Images 1989-2001 by Lippincott Williams Wilkins used by permission from SmartDraw.com.)...

Artificial neural networks often have a layered structure as shown in Figure 8.2 (b). The first layer is the input layer. The second layer is the hidden layer. The third layer is the output layer. Learning algorithms such as back-propagation that are described in many textbooks on neural networks (Kosko 1992 Rumelhart and McClelland 1986 Zell 1994) may be used to train such networks to compute a desired output for a given input. The networks are trained by adjusting the weights as well as the thresholds. 

Figure6.25 Schematicdrawingofan artificial neural network with a multilayer perceptron topology, showing the pathways from the input Xj to the output y , and the visible and hidden node layers.

Fig. 2. Structure of an artificial neural network. The network consists of three layers the input layer, the hidden layer, and the output layer. The input nodes take the values of the normalized QSAR descriptors. Each node in the hidden layer takes the weighted sum of the input nodes (represented as lines) and transforms the sum into an output value. The output node takes the weighted sum of these hidden node values and transforms the sum into an output value between 0 and 1.

One of the early problems with multilayer perceptrons was that it was not clear how to train them. The perception training rule doesn t apply directly to networks with hidden layers. Fortunately, Rumelhart and others (Rumelhart et al 1986) devised an intuitive method that quickly became adopted and revolutionized the field of artificial neural networks. The method is called back-propagation because it computes the error term as described above and propagates the error backward through the network so that weights to and from hidden units can be modified in a fashion similar to the delta rule for perceptions. 

Figure 14.2 Simple scheme of an artificial neural network with one hidden layer.

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... 

Fig. 4.14 Topology of a three-layered artificial neural network (ANN). The information flow is from left to right. The parameters representing a given compound are read into the input layer neurons from where the information is fed forward (weighted by v,j) to the neurons in the hidden layer, and so on. For clarity, not all connections...

In parallel to the SUBSTRUCT analysis, a three-layered artificial neural network was trained to classify CNS-i- and CNS- compounds. As mentioned previously, for any classification the descriptor selection is a cmcial step. Chose and Crippen published a compilation of 120 different descriptors, which were used to calculate AlogP values as weU as drug-likeness [53, 54]. Here, 92 of the 120 descriptors and the same datasets for training and tests as for the SUBSTRUCT algorithm were used. The network consisted of 92 input neurons, five hidden neurons, and one output neuron. 

Figure 3.10 Principal architecture of a three-layer artificial neural network (Aoyama and Ichikawa, 1991). A input layer with the number of input neurons corresponding to the number of parameters plus 1 B hidden layer with an arbitrary number of neurons C output layer with the number of output neurons corresponding to the number of categories in the respective classification problem.

Figure 10.5(b) Prediction with no variable selection. The experimental rationale was as for part (a), except that the artificial neural network was run on all 150 variables, that is, no variable selection was used. Optimization in this case resulted in having 8 nodes in the hidden layer the outputs were obtained after 10 000 epochs with an error on the calibration set of 0.01 6 out of 15 (40%) unadulterated samples and 12 out of 15 (80%) adulterated samples were predicted correctly. It may be seen that very poor separation was achieved - the two data bases do not line up on the predictive value of 0 or 1 but form a loose cloud in the middle area around 0.5, indicating that the net was unable to separate the two groups clearly. 

No chapter on modern chemometric methods would be complete without a mention of artificial neural networks (ANN). In a simple form these attempt to imitate the operation of neurons in the brain. Such networks have a number of linked layers of artificial neurons, including an input and an output layer (see Figure 8.13). The measured variables are presented to the input layer and are processed, by one or more intermediate ( hidden ) layers, to produce one or more outputs. For example, in inverse calibration, the inputs could be the absorbances at a number of wavelengths and the output could be the concentration of an analyte. The network is trained by an interactive procedure using a training set. Considering the example above, for each member of the training set the neural network predicts the concentration of the analyte. The discrepancy between the observed and predicted values... 

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. 

The multi-layer forward artificial neural network was firstly proposed by Minsky and Papert [103]. Cybenko [104] and Hornik et al. [105] have proved that multilayer forward networks with any munber of neurons of the ixia hidden layer can be close to any Borel continuous function. Moreover, if there are infinite neurons in the hidden layer, only one network of forward neurons is needed to approximate to any continuous function with arbitrary precision. So the multi-layer forward nemal network has been widely applied in function approximation [106]. 

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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