Linearly and quadratically separable classifiers using adaptive approach

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) is adaptively chosen and a hyperplane is constructed such that it separates the n-points at a margin ∈ and it best classifies the remaining points. The classification problem is formulated and three different algorithms are presented. Numerical results show that few iterations are sufficient for convergence. Further, the algorithm is extended to solve quadratically separable classification problems. The basic idea is based on mapping the physical space to another larger one where the problem becomes linearly separable.