Adaptive Iterative Approach Classifying Linearly and Quadratically Separable Sets

This paper presents a fast adaptive iterative algorithm to solve linearly separable classification problems in R (n) . In each iteration step, a subset of the sampling data (n-points) is adaptively chosen and a hyperplane is constructed such that it separates the n-points at a margin epsilon and it best classifies the remaining points. The classification problem is formulated and three different algorithms are presented. Further, the algorithm is extended to solve quadratically separable classification problems. The idea is based on mapping the physical space to another larger one where the problem becomes linearly separable. Various numerical illustrations and comparisons with other classification algorithms using benchmark datasets are presented. Numerical results show that few iteration steps are sufficient for convergence and demonstrate that the proposed approach achieves 100 \% correctness for linearly separable datasets, whereas other learning techniques may fail to achieve such percentage.