Finite Newton Method for Lagrangian Support Vector Machine Classi cation

Abstract

An implicit Lagrangian [19] formulation of a support vector machine classi er that led to a highly e ective iterative scheme [18] is solved here by a nite Newton method. The proposed method, which is extremely fast and terminates in 6 or 7 iterations, can handle classi cation problems in very high dimensional spaces, e.g. over 28,000, in a few seconds on a 400 MHz Pentium II machine. The method can also handle problems with large datasets and requires no specialized software other than a commonly available solver for a system of linear equations. Finite termination of the proposed method is established in this work.