Multilayer perceptron

The basic backpiopagation algorithm described above is, in practice, often very slow to converge. Moreover, just as Hopfield nets can sometimes get stuck in undesired spurious attractor states (i.e. local minima see section 10.6.5), so to can multilayer perceptrons get trapped in some undesired local minimum state. This is an unfortunate artifact that plagues all energy (or cost-function) minimization schemes. 

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... 

Figure 28.1 Diagram of a multilayer perceptron with one hidden layer.

Although the minimization of the objective function might run to convergence problems for different NN structures (such as backpropagation for multilayer perceptrons), here we will assume that step 3 of the NN algorithm unambiguously produces the best, unique model, g(x). The question we would like to address is what properties this model inherits from the NN algorithm and the specific choices that are forced. 

All of the studies above have used back propagation multilayer perceptrons and many other varieties of neural network exist that have been applied to PyMS data. These include minimal neural networks,117119 radial basis functions,114120 self-organizing feature maps,110121 and autoassociative neural networks.122123... 

Fig. 6.18. Schematic representation of a multilayer perceptron with two input neurons, three hidden neurons (with sigmoid transfer functions), and two output neurons (with sigmoid transfer functions, too)...

The most popular techniques of multilayer perceptrons (MLP) are back-propagation networks (Wythoff [1993] Jagemann [1998]). The weight matrixes W are estimated by minimizing the net error... 

Catasus et al. [67] studied two types of neural networks traditional multilayer perceptron neural networks and generalised regression neural networks (GRNNs) to correct for nonlinear matrix effects and long-term signal drift in ICP-AES. 

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.

Among the most wide-spread neural networks are feedforward networks, namely multilayer perceptron (MLP). This network type has been proven to be universal function approximators [11], Another important feature of MLP is the ability to generalization. Therefore MLP can be powerful tool for design of intrusion detection systems. 

We describe the intrusion detection system, which consists of two different neural networks. The first neural network is nonlinear PCA (principal component analysis) network, which permits to identify normal or anomalous system behavior. The second one is multilayer perceptron (MLP), which can recognize type of attack. 

The rest of the paper is organized as follows. The Section 2 describes attack classification and training data set. In the Section 3 the intrusion detection system is described, based on neural network approach. Section 4 presents the nonlinear PCA neural network and multilayer perceptron for identification and classification of computer network attack. In Section 5 the results of experiments are presented. Conclusion is given in Section 6. 

The neural network for identification is nonlinear PCA (NPCA) network [18]. As input data in this case, four features service, duration, src bytes, and dst bytes are used. The neural network for recognition is multilayer perceptron. In this case, all of the listed features above (Table 3) are used as input data. Such a system permits to identify and recognize the network attacks. 

Let s consider the neural network for recognition of attack. This network is multilayer perceptron with 6 input units, 40 hidden units and 23 output... 

Fig. 17. Use of a multilayer perceptron-type artificial neural network to analyze an interferometric image of...

Figure 5.3 Simple multilayered perceptron of an artificial neural network...

The characters are first normalized by rotating the original scanned image to correct for scanning error and by combinations of scaling under sampling and contrast and density adjustments of the scanned characters. In operation, the normalized characters are then presented to a multilayer perceptron neural network for recognition the network was trained on exemplars of characters form numerous serif and sans serif fonts to achieve font invariance. Where the output from the neural network indicates more than one option, for example 5 and s, the correct interpretation is determined from context. 

Usually complex structures with more than 15 layers are employed, called the multilayer perceptron (MLP). Some of the commercial programs which have been used to fit tableting parameters are INForm (Intelligensys, Billingham Teesside), CAD/Chem (AI Ware, Cleveland, OH), which is no longer commercially available, and the Neural Network Toolbox of MATLAB (MathWorks, Natick, MA). 

In the previous chapter a simple two-layer artificial neural network was illustrated. Such two-layer, feed-forward networks have an interesting history and are commonly called perceptrons. Similar networks with more than two layers are called multilayer perceptrons, often abbreviated as MLPs. In this chapter the development of perceptrons is sketched with a discussion of particular applications and limitations. Multilayer perceptron concepts are developed applications, limitations and extensions to other kinds of networks are discussed. 

Although perceptrons are quite useful for a wide variety of classification problems, their usefulness is limited to problems that are linearly separable problems in which a line, plane or hyperplane can effect the desired dichotomy. As an example of a non-linearly separable problem, see Figure 3.4. This is just Figure 3.1 with an extra point added (measure 1 =. 8 and measure 2 =. 9) but this point makes it inpossible to find a line that can separate the depressed from non-depressed. This is no longer a linearly separable problem, and a simple perceptron will not be able to find a solution. However, note that a simple curve can effectively separate the two groups. Multilayer perceptrons, discussed in the next section, can be used for classification, even in the presence of nonlinearities. 

After the Minsky and Papert book in 1969 (Minsky Papert, 1969) which clarified the linearity restrictions of perceptrons, little work was done with perceptrons. However, in 1986 McClelland and Rumelhart (McClelland Rumelhart, 1986) revived the field with multilayer perceptrons and an intuitive training algorithm called back-propagation (discussed in Chapter 5). 

Multilayer perceptrons (MLP) are perceptrons with more than two layers, Le., an input layer, an output layer and at least one layer between them. The middle layers are called... 

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