Eecient Perceptron Learning Using Constrained Steepest Descent Running Title: Eecient Perceptron Learning 1 Eecient Perceptron Learning Using Constrained Steepest Descent

| An algorithm is proposed for training the single-layered per-ceptron. The algorithm follows successive steepest descent directions with respect to the perceptron cost function, taking care not to increase the number of misclassiied patterns. The problem of nding these directions is stated as a quadratic programming task, to which a fast and eeective solution is proposed. The resulting algorithm has no free parameters and therefore no heuristics are involved in its application. It is proved that the algorithm always converges in a nite number of steps. For linearly separable problems, it always nds a hyperplane that completely separates patterns belonging to diierent categories. Termination of the algorithm without separating all given patterns means that the presented set of patterns is indeed linearly inseparable. Thus the algorithm provides a natural criterion for linear sepa-rability. Compared to other state of the art algorithms, the proposed method exhibits substantially improved speed, as demonstrated in a number of demanding benchmark classiication tasks.