Convergence properties of symmetric learning algorithm for pattern classification

The geometric learning algorithm (GLA) was proposed as an application of the affine projection algorithm (APA) for an adaptive filter to a perceptron. In the GLA, the connection weight vector w(n) is updated vertically towards the orthogonal complement of /spl kappa/ patterns. The GLA demonstrates some typical behavior when the learning rate /spl lambda/ is 2, which means that w(n) and w(n+1) are symmetric with respect to the complement. Therefore, in this paper, the GLA with /spl lambda/=2 is discriminated as a "symmetric learning algorithm (SLA)" and the convergence properties of the SLA are analyzed. The convergence condition among the order /spl kappa/ of the SLA, the number P of patterns and the dimension N of patterns is analyzed theoretically. It is proved that /spl kappa/