Evolutionary learning with kernels

In this paper we embed evolutionary computation into statistical learning theory. First, we outline the connection between large margin optimization and statistical learning and see why this paradigm is successful for many pattern recognition problems. We then embed evolutionary computation into the most prominent representative of this class of learning methods, namely into Support Vector Machines (SVM). In contrast to former applications of evolutionary algorithms to SVMs we do not only optimize the method or kernel parameters. We rather use both evolution strategies and particle swarm optimization in order to directly solve the posed constrained optimization problem. Transforming the problem into the Wolfe dual reduces the total runtime and allows the usage of kernel functions. Exploiting the knowledge about this optimization problem leads to a hybrid mutation which further decreases convergence time while classification accuracy is preserved. We will show that evolutionary SVMs are at least as accurate as their quadratic programming counterparts on six real-world benchmark data sets. The evolutionary SVM variants frequently outperform their quadratic programming competitors. Additionally, the proposed algorithm is more generic than existing traditional solutions since it will also work for non-positive semidefinite kernel functions and for several, possibly competing, performance criteria.