Optimizing an algebraic perceptron solution

In this paper ways of optimizing a solution achieved by the perceptron algorithm are investigated. The perceptron algorithm was successfully applied to polynomial inner-product kernels equivalent to those of support vector machines (SVM). Therefore, the algebraic perceptron can achieve a polynomial separation in the input data space by doing a linear separation in a high-dimensional feature space. Unlike the solution for the separating hyperplane of a SVM, a solution achieved by the algebraic perceptron will be nonoptimal in general. We improve an algebraic perceptron solution by mapping data points onto a sphere and then applying a standard C-SVM in form of the Adatron or Vijayakumar´s (1999) SVM-seq, respectively. As a consequence of this, there is no equality constraint in the C-SVM problem