Layer input

The architecture of a backpropagation neuronal network is comparatively simple. The network consists of different neurone layers. The layer connected to the network input is called input layer while the layer at the network output is called the output layer. The different layers between input and output are named hidden layers. The number of neurones in the layers is determined by the developer of the network. Networks used for classification have commonly as much input neurones as there are features and as much output neurones as there are classes to be separated. 

The architecture of a counter-propagation network resembles that of a Kohonen network, but in addition to the cubic Kohonen layer (input layer) it has an additional layer, the output layer. Thus, an input object consists of two parts, the m-dimeiisional input vector (just as for a Kohonen network) plus a second k-dimensional vector with the properties for the object. 

Figure 9-21. Counterpropagatlon network plotted as two boxes. The upper box contains the weights of the input layer, while the lower box contains those of the output layer.

During training the input layer is adapted as in a regular Kohonen network, i.c., the winning neuron is determined only on the basis of the input values. But in contra.st to the training of a Kohonen network, the output layer is also adapted, which gives an opportunity to use the network for prediction. 

The feedforward network shown in Figure 10.22 eonsists of a three neuron input layer, a two neuron output layer and a four neuron intermediate layer, ealled a hidden layer. Note that all neurons in a partieular layer are fully eonneeted to all neurons in the subsequent layer. This is generally ealled a fully eonneeted multilayer network, and there is no restrietion on the number of neurons in eaeh layer, and no restrietion on the number of hidden layers. 

Consider a three layer network. Let the input layer be layer one ( = 1), the hidden layer be layer two ( = 2) and the output layer be layer three ( = 3). The baek-propagation eommenees with layer three where dj is known and henee 8j ean be ealeulated using equation (10.69), and the weights adjusted using equation (10.71). To adjust the weights on the hidden layer = 2) equation (10.69) is replaeed by... 

The ANN model had four neurones in the input layer one for each operating variable and one for the bias. The output was selected to be cumulative mass distribution thirteen neurones were used to represent it. A sigmoid functional... 

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

Being able to construct an e xplicit solution to a nonlinearly separable problem such as the XOR-problem by using a multi-layer variant of the simple perceptron does not, of course, guarantee that a multi-layer perceptron can by itself learn the XOR function. We need to find a learning rule that works not just for information that only propagates from an input layer to an output layer, but one that works for information that propagates through an arbitrary number of hidden layers as well. 

We are now ready to introduce the backpropagation learning rule (also called the generalized delta rule) for multidayercd perceptrons, credited to Rumelhart and McClelland [rumel86a]. Figure 10.12 shows a schematic of the multi-layered per-ceptron s structure. Notice that the design shown, and the only kind we will consider in this chapter, is strictly feed-forward. That is to say, information always flows from the input layer to each hidden layer, in turn, and out into the output layer. There are no feedback loops anywhere in the system. 

Just as was the case with simple perceptrons, the multi-layer perceptron s fundamental problem is to learn to associate given inputs with desired outputs. The input layer consists of as many neurons as are necessary to set up some natural... 

Step 2 Set the input layer equal to the input values of the first input/output fact pair i.e. let... 

The general stmcture is shown in Fig. 44.9. The units are ordered in layers. There are three types of layers the input layer, the output layer and the hidden layer(s). All units from one layer are connected to all units of the following layer. The network receives the input signals through the input layer. Information is then passed to the hidden layer(s) and finally to the output layer that produces the response of the network. There may be zero, one or more hidden layers. Networks with one hidden layer make up the vast majority of the networks. The number of units in the input layer is determined by p, the number of variables in the (nxp) matrix X. The number of units in the output layer is determined by q, the number of variables in the inxq) matrix Y, the solution pattern. 

The signal propagation in the MLF networks is similar to that of the perceptron-like networks, described in Section 44.4.1. For each object, each unit in the input layer is fed with one variable of the X matrix and each unit in the output layer is intended to provide one variable of the Y table. The values of the input units are passed unchanged to each unit of the hidden layer. The propagation of the signal from there on can be summarized in three steps. 

Each hidden unit,y, receives the signals from the p units of the previous layer, the input layer. From these signals the net input is calculated ... 

Radial basis function networks (RBF) are a variant of three-layer feed forward networks (see Fig 44.18). They contain a pass-through input layer, a hidden layer and an output layer. A different approach for modelling the data is used. The transfer function in the hidden layer of RBF networks is called the kernel or basis function. For a detailed description the reader is referred to references [62,63]. Each node in the hidden unit contains thus such a kernel function. The main difference between the transfer function in MLF and the kernel function in RBF is that the latter (usually a Gaussian function) defines an ellipsoid in the input space. Whereas basically the MLF network divides the input space into regions via hyperplanes (see e.g. Figs. 44.12c and d), RBF networks divide the input space into hyperspheres by means of the kernel function with specified widths and centres. This can be compared with the density or potential methods in pattern recognition (see Section 33.2.5). 

Of the several approaches that draw upon this general description, radial basis function networks (RBFNs) (Leonard and Kramer, 1991) are probably the best-known. RBFNs are similar in architecture to back propagation networks (BPNs) in that they consist of an input layer, a single hidden layer, and an output layer. The hidden layer makes use of Gaussian basis functions that result in inputs projected on a hypersphere instead of a hyperplane. RBFNs therefore generate spherical clusters in the input data space, as illustrated in Fig. 12. These clusters are generally referred to as receptive fields. 

An ANN is an array of three or more interconnected layers of cells called nodes (much like columns of cells in a spreadsheet). Data are introduced to the ANN through the nodes of the input layer. For instance, each input layer node can contain the relative intensity of one of the m/z values from a bacterial pyrolysis mass spectrum. The output layer nodes can be assigned to iden-... 

The input layer, their neurons correspond to the prediction variables (the analytical values x,-) input layers are counted to be layer 0... 

One layer of input nodes and another of output nodes form the bookends to one or more layers of hidden nodes Signals flow from the input layer to the hidden nodes, where they are processed, and then on to the output nodes, which feed the response of the network out to the user. There are no recursive links in the network that could feed signals from a "later" node to an "earlier" one or return the output from a node to itself. Because the messages in this type of layered network move only in the forward direction when input data are processed, this is known as a feedforward network. 

Input layer Hidden layer Output layer... 

Assign to each node in the input layer the appropriate value in the input vector. Feed this input to all nodes in the first hidden layer. 

The structure of a SOM is different from that of the feedforward network. Instead of the layered structure of the feedforward network, there is a single layer of nodes, which functions both as an input layer and an output layer. In a feedforward network, each node performs a processing task, accepting input, processing it, and generating an output signal. By contrast, in a SOM, every node stores a vector whose dimensionality and type matches that of the samples. Thus, if the samples consist of infrared spectra, each node on the SOM stores a pseudo-infrared spectrum (Figure 12). The spectra at the nodes are refined as the network learns about the data in the database and the vector at each node eventually becomes a blended composite of all spectra in the database. 

This type of network is composed of an input layer, an output layer and one or more hidden layers (figure 1). Bias term in each layer is analogous to the constant term of any polynomial. The number of neurons in the input and the output layer depends on the respective number of input and output parameters taken into consideration. However, the hidden layer may contain zero or more neurons. All the layers are interconnected as shown in the figure and the strength of these interconnections is determined by the weights associated with them. The output from a neuron in the hidden layer is the transformation of the weighted sum of output from the input layers and is given as (1)... 

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. 

The number of neurons in the hidden layer was therefore increased systematically. It was found that a network of one hidden layer consisting of twenty neurons, as shown in Figure 2.6, performed well for both the training and testing data set. More details about the performance of this network will be given later. The network architecture depicted in Figure 2.6 consists of an input layer, a hidden layer, and an output layer. Each neuron in the input layer corresponds to a particular feed property. The neurons... 

Input Layer Hidden Layer Output Layer... 

Fig. 7. Artificial neural network model. Bioactivities and descriptor values are the input and a final model is the output. Numerical values enter through the input layer, pass through the neurons, and are transformed into output values the connections (arrows) are the numerical weights. As the model is trained on the Training Set, the system-dependent variables of the neurons and the weights are determined.

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