ASYMPTOTIC LEVEL DENSITY IN TOPOLOGICAL FEATURE MAPS

被引:35
作者
DERSCH, DR
TAVAN, P
机构
[1] Institut für Medizinische Optik, Theoretische Biophysik, Ludwig-Maximilians-Universität München
来源
IEEE TRANSACTIONS ON NEURAL NETWORKS | 1995年 / 6卷 / 01期
关键词
D O I
10.1109/72.363433
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The Kohonen algorithm entails a topology conserving mapping of an input pattern space X subset of R(n) characterized by an a priori probability distribution P(x), x is an element of X, onto a discrete lattice of neurons tau with virtual positions w(tau)is an element of X. Extending results obtained by Ritter [4] we show in the one-dimensional case for an arbitrary monotonously decreasing neighborhood function h(\tau - tau'\) that the point density D(w(tau)) of the virtual net is a polynomial function of the probability density P(x) with D(w(tau)) similar to P-alpha(w(tau)). 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.
引用
收藏
页码:230 / 236
页数:7
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