Yin H, Allinson N M
Department of Electronics, University of York, United Kingdom.
Neural Comput. 1995 Nov;7(6):1178-87. doi: 10.1162/neco.1995.7.6.1178.
In this paper an analysis of the statistical and the convergence properties of Kohonen's self-organizing map of any dimension is presented. Every feature in the map is considered as a sum of a number of random variables. We extend the Central Limit Theorem to a particular case, which is then applied to prove that the feature space during learning tends to multiple gaussian distributed stochastic processes, which will eventually converge in the mean-square sense to the probabilistic centers of input subsets to form a quantization mapping with a minimum mean squared distortion either globally or locally. The diminishing effect, as training progresses, of the initial states on the value of the feature map is also shown.
本文对任意维度的Kohonen自组织映射的统计特性和收敛特性进行了分析。映射中的每个特征都被视为多个随机变量的和。我们将中心极限定理扩展到一种特殊情况，然后应用该定理证明学习过程中的特征空间趋向于多个高斯分布的随机过程，这些过程最终将在均方意义上收敛到输入子集的概率中心，以形成全局或局部具有最小均方失真的量化映射。还展示了随着训练的进行，初始状态对特征映射值的影响逐渐减小。
