Nonlinear PCA

Techniques for multivariate input analysis reduce the data dimensionality by projecting the variables on a linear or nonlinear hypersurface and then describe the input data with a smaller number of attributes of the hypersurface. Among the most popular methods based on linear projection is principal component analysis (PCA). Those based on nonlinear projection are nonlinear PCA (NLPCA) and clustering methods. 

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. 

As it is mentioned before, the goal of nonlinear PCA network (NPCA) is to identify an attack. The NPCA architecture consists of five fully connected layers with 3 input nodes and 3 output units. The number of nodes in the hidden layers is shown in Figure 2. 

PCA is not the only projection method that can be used. Various types of nonlinear projections have been employed, e.g., Sammon mapping and nonlinear PCA [80], and several software packages can be used to graphically visualize library distributions and aid compound selection [81]. 

Autoassociative neural networks provide a special five-layer network structure (Figure 3.6) that can implement nonlinear PCA by reducing variable dimensionality and producing a feature space map that retains the maximum possible amount of information from the original data set [150]. Autoassociative neural networks use conventional feedforward connections and sigmoidal or linear nodal transfer functions. 

Nonlinear PCA To address the nonlinearity in the identity mapping of multivariate data, a nonlinear counterpart of the PCA can be used (see Section 3.6.1). As the versions of NLPCA make use of the neural network (NN) concept to address the nonlinearity, they suffer from the known overparameterization problem in the case of noise corrupted data. Data with small SNR will also give rise to extensive computations during the training of the network. Shao et al. [266] used wavelet filtering to pre-process the data followed by IT-net to detect the non-conforming trends in an industrial spray drier. 

Once a calibration model for the process space is built using the lin-ear/nonlinear PCA, over the course of operation, the SPE can be used to monitor the process against any unanticipated disturbances and/or sensor failures. At times when the SPEumit is violated, instead of evaluating the variable contribution to the SPE, one can go one step back in each sensor array and calculate the SPE again. Subsequently, the SPE values are ordered from minimum to maximum. In other words, following vectors are defined first. 

EC Malthouse. Limitations of nonlinear PCA as performed with generic neural networks. IEEE Trans, on Neural Networks, 9(1) 165-173, 1998. 

While PCA is a linear projection method, there also exist nonlinear projection methods, e.g. multidimensional scaling [Mardia et al. 1979] and nonlinear PCA [Dong McAvoy 1996], A good overview of nonlinear multivariate analysis tools is given by [Gift 1990],... 

Licciardi G, Marpu PR, Chanussot J, Benediktsson JA (2012) Linear versus nonlinear PCA for the classification of hyperspectral data based on the extended morphological profiles. IEEE Geosci Remote Sens Lett 9(3) 447 51... 

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