Nonlinear system neural networks

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. 

No quantitative applications of neural networks to quantitative analysis of linear systems have been reported where the results have been significantly better than those obtained by PLS, as would be expected since PLS (and indeed, the other multivariate methods described in this chapter) have been designed explicitly to handle linear systems. Analogous techniques, such as polynomial PLS or spline PLS, have been designed for nonlinear systems. It is interesting that with nonlinear data, neural networks have been shown to outperform any of the linear or nonlinear PLS techniques [27]. 

The second main category of neural networks is the feedforward type. In this type of network, the signals go in only one direction there are no loops in the system as shown in Fig. 3. The earliest neural network models were linear feed forward. In 1972, two simultaneous articles independently proposed the same model for an associative memory, the linear associator. J. A. Anderson [17], neurophysiologist, and Teuvo Kohonen [18], an electrical engineer, were unaware of each other s work. Today, the most commonly used neural networks are nonlinear feed-forward models. 

Neural networks are applied in analytical chemistry in many and diverse ways. Used in calibration, ANNs have especially advantages in case of nonlinear relationships, multicomponent systems and single component analysis in case of various disturbances. 

It is possible to show that when the different parts of a system are connected by nonlinear interactions, one can again obtain oscillation in concentrations, patterns of chemical substances in space, and wave propagation. These phenomena are important in some biological problems when the reaction-diffusion mechanisms cannot give an adequate description of the system. Morphogenetic fields and neural networks are examples of such systems. 

L. Hadjiiski, P. Geladi and Ph. Hopke, A comparison of modelling nonlinear systems with artificial neural networks and partial least squares, Chemom. Intell. Lab. Syst., 49, 1999, 91-103. 

M. Blanco, J. Coello, H. Iturriaga, S. Maspoch and J. Pages, NIR calibration in nonlinear systems by different PLS approaches and artificial neural networks, Chemom. Intell. Lab. Syst., 50(1), 2000, 75-82. 

This paper presents applying of neural networks for intrusion detection through an examination of network traffic data. It has been shown that denial of service and other network-based attacks are presented in the network traffic data. Therefore using neural networks permits to extract nonlinear relationships between variables from network traffic and to design real-time 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 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. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

State feedback control is commonly used in control systems, due to its simple structure and powerful functions. Data-driven methods such as neural networks are useful only for situations with fully measured state variables. For this system in which state variables are not measurable and measurement function is nonlinear, we are dependant on system model for state estimation. On the other hand, as shown in figure 2, in open-loop situations, system has limit cycle behavior and measurements do not give any information of system dynamics. Therefore, we use model-based approach. 

Methods Using 2D and ID Descriptors A good number of articles on aqueous solubility used a nonlinear method of data analysis, in particular, for methods developed with ID and 2D descriptors. Huuskonen [16] used E-state indexes [52,53] and several other topological indexes, with a total of 30 indexes, to develop his models. The predicted results for the 413 test set, SE = 0.71, calculated with MLRA were improved with a neural network, resulting in SE = 0.6. Tetko [17] noticed that E-state indexes represent a complete system of descriptors for molecules, and thus only these descriptors are sufficient to develop the aqueous solubility model. Indeed the model developed by the authors using exclusively E-state indexes provides similar results when compared to the model of Huuskonen [16]. Later on, the model was redeveloped using the Associative Neural Network (ASNN) method [54],... 

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