| C++ Neural Networks and Fuzzy Logic |
by Valluru B. Rao
M&T Books, IDG Books Worldwide, Inc.
ISBN: 1558515526 Pub Date: 06/01/95
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You were introduced in the preceding pages to the Perceptron model, the Feedforward network, and the Hopfield network. You learned that the differences between the models lie in their architecture, encoding, and recall. We aim now to give you a comprehensive picture of these and other neural network models. We will show details and implementations of some networks in later chapters.
The models we briefly review in this chapter are the Perceptron, Hopfield, Adaline, Feed-Forward Backpropagation, Bidirectional Associative Memory, Brain-State-in-a-Box, Neocognitron, Fuzzy Associative Memory, ART1, and ART2. C++ implementations of some of these and the role of fuzzy logic in some will be treated in the subsequent chapters. For now, our discussion will be about the distinguishing characteristics of a neural network. We will follow it with the description of some of the models.
A neural network has its neurons divided into subgroups, or fields, and elements in each subgroup are placed in a row, or a column, in the diagram depicting the network. Each subgroup is then referred to as a layer of neurons in the network. A great many models of neural networks have two layers, quite a few have one layer, and some have three or more layers. A number of additional, so-called hidden layers are possible in some networks, such as the Feed-forward backpropagation network. When the network has a single layer, the input signals are received at that layer, processing is done by its neurons, and output is generated at that layer. When more than one layer is present, the first field is for the neurons that supply the input signals for the neurons in the next layer.
Every network has a layer of input neurons, but in most of the networks, the sole purpose of these neurons is to feed the input to the next layer of neurons. However, there are feedback connections, or recurrent connections in some networks, so that the neurons in the input layer may also do some processing. In the Hopfield network you saw earlier, the input and output layers are the same. If any layer is present between the input and output layers, it may be referred to as a hidden layer in general, or as a layer with a special name taken after the researcher who proposed its inclusion to achieve certain performance from the network. Examples are the Grossberg and the Kohonen layers. The number of hidden layers is not limited except by the scope of the problem being addressed by the neural network.
A layer is also referred to as a field. Then the different layers can be designated as field A, field B, and so on, or shortly, FA, FB.
A neural network with a single layer is also capable of processing for some important applications, such as integrated circuit implementations or assembly line control. The most common capability of the different models of neural networks is pattern recognition. But one network, called the Brain-State-in-a-Box, which is a single-layer neural network, can do pattern completion. Adaline is a network with A and B fields of neurons, but aggregation or processing of input signals is done only by the field B neurons.
The Hopfield network is a single-layer neural network. The Hopfield network makes an association between different patterns (heteroassociation) or associates a pattern with itself (autoassociation). You may characterize this as being able to recognize a given pattern. The idea of viewing it as a case of pattern recognition becomes more relevant if a pattern is presented with some noise, meaning that there is some slight deformation in the pattern, and if the network is able to relate it to the correct pattern.
The Perceptron technically has two layers, but has only one group of weights. We therefore still refer to it as a single-layer network. The second layer consists solely of the output neuron, and the first layer consists of the neurons that receive input(s). Also, the neurons in the same layer, the input layer in this case, are not interconnected, that is, no connections are made between two neurons in that same layer. On the other hand, in the Hopfield network, there is no separate output layer, and hence, it is strictly a single-layer network. In addition, the neurons are all fully connected with one another.
Let us spend more time on the single-layer Perceptron model and discuss its limitations, and thereby motivate the study of multilayer networks.
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