Perceptron-Like Performance for Intersections of Halfspaces

Abstract

Given a set of examples on the unit ball in Rn which are labelled by a halfspace h which has margin ρ (minimum Euclidean distance from any point to the separating hyperplane), the well known Perceptron algorithm finds a separating hyperplane. The Perceptron Convergence Theorem (see e.g. [2]) states that at most 4/ρ 2 iterations of the Perceptron update rule are required, and thus the algorithm runs in time \(O(\frac{n}{\rho^{2}})\).