Dersch D R, Tavan P
Inst. fur Medizinische Optik, Theor. Biophys., Ludwig-Maximilians-Univ., Munchen.
IEEE Trans Neural Netw. 1995;6(1):230-6. doi: 10.1109/72.363433.
The Kohonen algorithm entails a topology conserving mapping of an input pattern space X subsetR(n) characterized by an a priori probability distribution P(x), xinX, onto a discrete lattice of neurons r with virtual positions w(r)inX. Extending results obtained by Ritter (1991) the authors show in the one-dimensional case for an arbitrary monotonously decreasing neighborhood function h(|r-r'|) that the point density D(W(r)) of the virtual net is a polynomial function of the probability density P(x) with D(w(r))~P(alpha)(w(r)). Here the distortion exponent is given by alpha=(1+12R)/3(1+6R) and is determined by the normalized second moment R of the neighborhood function. A Gaussian neighborhood interaction is discussed and the analytical results are checked by means of computer simulations.
科霍宁算法需要将一个由先验概率分布(P(x))（(x\in X)）表征的输入模式空间(X\subseteq R(n))进行拓扑保持映射，映射到具有虚拟位置(w(r)\in X)的离散神经元格(r)上。扩展里特（1991年）获得的结果，作者在一维情况下针对任意单调递减的邻域函数(h(|r - r'|))表明，虚拟网络的点密度(D(W(r)))是概率密度(P(x))的多项式函数，其中(D(w(r))\sim P^{\alpha}(w(r)))。这里，失真指数由(\alpha = (1 + 12R)/3(1 + 6R))给出，并且由邻域函数的归一化二阶矩(R)确定。讨论了高斯邻域相互作用，并通过计算机模拟检验了分析结果。
