A Survey of Outlier Detection Methods in Network Anomaly Identification <s> Definition 6: <s> In this letter we discuss a least squares version for support vector machine (SVM) classifiers. Due to equality type constraints in the formulation, the solution follows from solving a set of linear equations, instead of quadratic programming for classical SVM‘s. The approach is illustrated on a two-spiral benchmark classification problem. <s> BIB001 </s> A Survey of Outlier Detection Methods in Network Anomaly Identification <s> Definition 6: <s> Recently, applying artificial intelligence, machine learning and data mining techniques to intrusion detection system are increasing. But most of researches are focused on improving the performance of classifier. Selecting important features from input data lead to a simplification of the problem, faster and more accurate detection rates. Thus, selecting important features is an important issue in intrusion detection. Another issue in intrusion detection is that most of the intrusion detection systems are performed by off-line and it is not proper method for realtime intrusion detection system. In this paper, we develop the realtime intrusion detection system which combines on-line feature extraction method with least squares support vector machine classifier. Applying proposed system to KDD CUP 99 data, experimental results show that it has remarkable performance compared to off-line intrusion detection system. <s> BIB002
Let X and Y be sets and let f be a function from X to Y . Elements x 1 and x 2 of X are equivalent if f (x 1 ) and f (x 2 ) are equal, i.e., they are the same element of Y  . Formally: The kernel function K(x, y) can be expressed as a dot product in a high dimensional space. If the arguments to the kernel are in a measurable space X, and if the kernel is positive semi-definite, i.e., . . , c n ) of objects, there exists a function ϕ(x) whose range is in an inner product space of possibly high dimension, such that The KPCA (Kernel Principal Component Analysis) BIB002 is a real time IDS. It is composed of two parts. First part is used for on-line feature extraction. The second part is used for classification. Extracted features are used as input for classification. With an adaptation of the kernel function kernel-trick (Equation 19 ) KPCA extracts on-line non-linear features. Here, Least Squares Support Vector Machines (LS-SVM) BIB001 is used as a classifier. SVMs typically solve problems by quadratic programming (QP). Solving QP problem requires complicated computational effort and has high memory requirement. LS-SVM overcomes by solving a set of linear equations.