Convergence models for Rosenblatt's perceptron learning algorithm
Suhas N. Diggavi, John J. Shynk, N.J. Bershad · IEEE Transactions on Signal Processing · 1995
Presents a stochastic analysis of the steady-state and transient convergence properties of a single-layer perceptron for fast learning (large step-size, input-power product). The training data are modeled using a system identification formulation with zero-mean Gaussian inputs. The perceptron weights are adjusted by a learning algorithm equivalent to Rosenblatt's perceptron convergence procedure. It is shown that the convergence points of the algorithm depend on the step size /spl mu/ and the input signal power (variance) /spl sigma//sub x//sup 2/, and that the algorithm is stable essentially for /spl mu/>0. Two coupled nonlinear recursions are derived that accurately model the transient behavior of the algorithm. The authors also examine how these convergence results are affected by noisy perceptron input vectors. Computer simulations are presented to verify the analytical models.>