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On two-point boundary conditions in optimal control problems

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2004年第2期122卷 425-432页

作者： Ahmadinia, M Radjabalipour, M Ghom Univ Dept Math Ghom Iran Univ Kerman Dept Math Kerman Iran Univ Toronto Dept Math Toronto ON M5S 1A1 Canada

Let. (x)over dot = g(t, x(t), u(t)) be the governing equation of an optimal control problem with two-point boundary conditions h(0)(x(a)) + h(1)(x(b)) = 0, where x:[a, b] --> R-n is continuous, u:[a, b] --> Rk-n is piecewise continuous and left continuous, h(0), h(1) : R-n --> R-q are continuously differentiable, and g:[a, b] x R-k --> R-n is continuous. The paper finds functions xi(i) is an element ofC(1)([a, b] x R-n) such that (x(t), u(t)) is a solution of the governing equation if and only if integral(a)(b) [(partial derivativexi(i)/partial derivativex)g + partial derivativexi(i)/partial derivativet]dt = 0, i = 1, 2, 3,....

关键词： Riesz representation theorem optimal control problems two-point boundary conditions linear programming mixed 0-1 integer linear programming

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A Comparison of Feature-Selection Methods for Intrusion Detection

A Comparison of Feature-Selection Methods for Intrusion Dete...

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5th International Conference on Mathematical Methods, Models and Architectures for Computer Network Security

作者： Nguyen, Hai Thanh Petrovic, Slobodan Franke, Katrin Gjovik Univ Coll Norwegian Informat Secur Lab Gjovik Norway

ISBN: (纸本)9783642147050

Feature selection is an important pre-processing step in intrusion detection Achieving reduction of the number of relevant traffic features without negative effect on classification accuracy is a goal that greatly improves overall effectiveness of an intrusion detection system A major challenge is to choose appropriate feature-selection methods that can precisely determine the relevance of features to the intrusion detection task and the redundancy between features Two new feature selection measures suitable for the intrusion detection task have been proposed recently [11,12] the correlation-feature-selection (CFS) measure and the minimal-redundancy-maximal-relevance (mRMR) measure In this paper, we validate these feature selection measures by comparing them with various previously known automatic feature-selection algorithms for intrusion detection The feature-selection algorithms involved in this comparison are the previously known SVM-wrapper, Markov-blanket and Classification & Regression Trees (CART) algorithms as well as the recently proposed generic-feature-selection (GeFS) method with 2 instances applicable in intrusion detection the correlation-feature-selection (GeFSCFS) and the minimal-redundancy-maximal-relevance (GeFSmRMR) measures Experimental results obtained over the KDD CUP'99 data set show that the generic-feature-selection (GeFS) method for intrusion detection outperforms the existing approaches by removing more than 30% of redundant features from the original data set, while keeping or yielding an even better classification accuracy

关键词： intrusion detection feature selection polynomial mixed 0-1 fractional programming mixed 0-1 integer linear programming

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Improving Effectiveness of Intrusion Detection by Correlation Feature Selection

Improving Effectiveness of Intrusion Detection by Correlatio...

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5th International Conference on Availability, Reliability and Security

作者： Nguyen, Hai Franke, Katrin Petrovic, Slobodan Gjovik Univ Coll NISlab Dept Comp Sci & Media Technol N-2802 Gjovik Norway

ISBN: (纸本)9780769539652

The quality of the feature selection algorithm is one of the most important factors that affects the effectiveness of an intrusion detection system (IDS). Achieving reduction of the number of relevant traffic features without negative effect on classification accuracy is a goal that greatly improves the overall effectiveness of the IDS. Obtaining a good feature set automatically without involving expert knowledge is a complex task. In this paper, we propose an automatic feature selection procedure based on the filter method used in machine learning. In particular, we focus on Correlation Feature Selection (CFS). By transforming the CFS optimization problem into a polynomial mixed 0 - 1 fractional programming problem and by introducing additional variables in the problem transformed in such a way, we obtain a new mixed 0 - 1 linear programming problem with a number of constraints and variables that is linear in the number of full set features. The mixed 0 - 1 linear programming problem can then be solved by means of branch-and-bound algorithm. Our feature selection algorithm was compared experimentally with the best-first-CFS and the genetic-algorithm-CFS methods regarding the feature selection capabilities. The classification accuracy obtained after the feature selection by means of the C4.5 and the BayesNet machines over the KDD CUP'99 IDS benchmarking data set was also tested. Experiments show that our proposed method outperforms the best first and genetic algorithm search strategies by removing much more redundant features and still keeping the classification accuracies or even getting better performances.

关键词： intrusion detection correlation-based feature selection polynomial mixed 0-1 fractional programming mixed 0-1 integer linear programming

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Improving Effectiveness of Intrusion Detection by Correlation Feature Selection

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INTERNATIONAL JOURNAL OF MOBILE COMPUTING AND MULTIMEDIA COMMUNICATIONS 2011年第1期3卷 21-34页

作者： Hai Thanh Nguyen Franke, Katrin Petrovic, Slobodan Gjovik Univ Coll Dept Comp Sci & Media Technol Informat Secur NISlab Gjovik Norway

In this paper, the authors propose a new feature selection procedure for intrusion detection, which is based on filter method used in machine learning. They focus on Correlation Feature Selection (CFS) and transform the problem of feature selection by means of CFS measure into a mixed 0-1 linear programming problem with a number of constraints and variables that is linear in the number of full set features. The mixed 0-1 linear programming problem can then be solved by using branch-and-bound algorithm. This feature selection algorithm was compared experimentally with the best-first-CFS and the genetic-algorithm-CFS methods regarding the feature selection capabilities. Classification accuracies obtained after the feature selection by means of the C4.5 and the BayesNet over the KDD CUP'99 dataset were also tested. Experiments show that the authors' method outperforms the best-first-CFS and the genetic-algorithm-CFS methods by removing much more redundant features while keeping the classification accuracies or getting better performances.

关键词： Correlation-Based Feature Selection Intrusion Detection mixed 0-1 integer linear programming Polynomial mixed 0-1 Fractional programming programming

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