Linearly and Quadratically Separable Classifiers Using Adaptive Approach

Abstract

This paper presents a fast adaptive iterative algorithm to solve linearly separable classification problems in ${R^n}$. 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.