Operations research: an introduction, 4th ed.
Operations research: an introduction, 4th ed.
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Introduction to Artificial Neural Systems
Introduction to Artificial Neural Systems
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Pattern Recognition, Third Edition
Pattern Recognition, Third Edition
Data Mining: Practical Machine Learning Tools and Techniques, Second Edition (Morgan Kaufmann Series in Data Management Systems)
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
IEEE Transactions on Neural Networks
The linear separability problem: some testing methods
IEEE Transactions on Neural Networks
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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.