多层感知机分类器行为延拓线性分析及其应用

An Analysis of Behaviors of Multilayer Perceptron Classifiers and Weight Initializing on A Hypersphere

严谨的线性判别函数与判别面的理论 ,适用于线性阈值 (MP模型 )神经元分类行为分析。本文将此理论扩展到非线性 sigmoid神经元 ,分析了用来解决模式分类问题的、由 sigmoid神经元构成的单隐层 MLP(多层感知机 )的内部行为 ;并通过一系列近似推理与实验验证 ,提出了将隐层权重矢量初始值均匀地分布在权重空间的一个圆 (超球面 )上的方法。针对几个困难的分类问题的实验表明 ,该方法抓住了 MLP分类器内部行为的重要特征 ,它使 MLP分类器跨越了可能存在的学习难点 ,把学习起点放在达到目标较简便的路经上。此方法在理论上简单直接 ,应用上方便有效 ,具有一定的普遍性。

The rigorous theory of linear discriminant function and decision surface is suitable for the analysis of linear neurons with threshold activation function used as linear classifiers. Extending this theory, this paper analyzes the sigmoidal neurons and the internal behaviors of single hidden-layer perceptrons (MLPs) with sigmoid neurons trained for pattern classifications. Based on a series of approximate reasoning and experiment verifications, the method of initializing weights is inducted. The proposed method of initializing input-to-hidden weight vectors{W-j} distributing uniformly on a circle (a hypersphere for a high-dimensional space) in the Wspace should be considered as a general method to a very marked degree for MLP classifiers. Several experiments of difficult pattern classification problems have justified its usefulness for the improvements of the performance of MLP classifiers. The proposed method may catch the main characters of MLP- classifiers and put the start point of learning on a shortcut of converge, and it is simple and clear on theory and convenient on applications.