Stochastic convergence analysis of the single-layer backpropagation algorithm for noisy input data

作     者：Bershad, NJ Cubaud, N Shynk, JJ 

作者机构：UNIV CALIF SANTA BARBARADEPT ELECT & COMP ENGNSANTA BARBARACA 93106 

出 版 物：《IEEE TRANSACTIONS ON SIGNAL PROCESSING》 (IEEE Trans Signal Process)

年 卷 期：1996年第44卷第5期

页      面：1315-1319页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 

主　　题：Stochastic processes Convergence Training data Signal to noise ratio Stochastic resonance Statistical learning Backpropagation algorithms Algorithm design and analysis System identification Transient analysis 

摘      要：The statistical learning behavior of the single-layer backpropagation algorithm was recently analyzed for a system identification formulation for noise-free training data, Transient and steady-state results were obtained for the mean weight behavior, mean-square error (MSE), and probability of correct classification. This correspondence extends these results to the case of noisy training data, Three new analytical results are obtained -1) the mean weights converge to finite values, 2) the MSE is bounded away from zero, and 3) the probability of correct classification does not converge to unity. However, over a wide range of signal-to-noise ratio (SNR), the noisy training data does not have a significant effect on the perceptron stationary points relative to the weight fluctuations. Hence, one concludes that noisy training data has a relatively small effect on the ability of the perceptron to learn the underlyingweight vector F of the training signal model.