›› 2011, Vol. 26 ›› Issue (5): 908-918.doi: 10.1007/s11390-011-0188-x

• Artificial Intelligence • Previous Articles    

Linearly and Quadratically Separable Classifiers Using Adaptive Approach

Mohamed Abdel-Kawy Mohamed Ali Soliman1 and Rasha M. Abo-Bakr2   

  1. 1. Department of Computer and Systems Engineering, Faculty of Engineering, Zagazig University, Zagazig, Egypt
    2. Departement of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
  • Received:2009-10-03 Revised:2011-05-14 Online:2011-09-05 Published:2011-09-05
  • Contact: Mohamed Abdel-Kawy Mohamed Ali Soliman E-mail:mamas2000@hotmail.com; rasha_abobakr@hotmail.com
  • About author:Mohamed Abdel-Kawy Mohamed Ali Soliman received the B.S. degree in electrical and electronic engineering from M.T.C (Military Technical College), Cairo, Egypt, with grade (Excellent) in 1974, the M.S. degree in electronic and communications engineering from Faculty of Engineering, Cairo University, Egypt, with the research on "observers in modern control systems theory", 1985, and the Ph.D. degree in aeronautical engineering, the thesis title is "Intelligent Management for Aircraft and Spacecraft Sensors Systems", 2000. He is currently head of Computer and Systems Engineering Department, Faculty of Engineering, Zagazig University. His research interests lie in the intersection of the general fields of computer science and engineering, brain science, and cognitive science.
    Rasha M. Abo-Bakr was born in 1976 in Egypt, received her Bachelor's degree from Mathematics (Computer Science) Department, Faculty of Science, Zagazig University, Egypt. She was also awarded her Master's degree in computer science in 2003, with a thesis titled "Computer Algorithms for System Identification". Since 2003 she has been an assistant lecturer at Mathematics (Computer Science) Department, Faculty of Science, Zagazig University. She received her Ph.D. degree in mathematics & computer science from Zagazig University, in 2011, with a dissertation titled "Symbolic Modeling of Dynamical Systems Using Soft Computing Techniques". Her research interests are artificial intelligence, soft computing technologies, and astronomy.

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This paper presents a fast adaptive iterative algorithm to solve linearly separable classification problems in Rn. In each iteration, a subset of the sampling data (n-points, where n is the number of features) is adaptively chosen and a hyperplane is constructed such that it separates the chosen n-points at a margin ε and best classifies the remaining points. The classification problem is formulated and the details of the algorithm are presented. Further, the algorithm is extended to solving quadratically separable classification problems. The basic idea is based on mapping the physical space to another larger one where the problem becomes linearly separable. Numerical illustrations show that few iteration steps are sufficient for convergence when classes are linearly separable. For nonlinearly separable data, given a specified maximum number of iteration steps, the algorithm returns the best hyperplane that minimizes the number of misclassified points occurring through these steps. Comparisons with other machine learning algorithms on practical and benchmark datasets are also presented, showing the performance of the proposed algorithm.

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