Lee John A, Verleysen Michel
Department of Electricity, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
Neural Netw. 2002 Oct-Nov;15(8-9):993-1003. doi: 10.1016/s0893-6080(02)00073-4.
Self-organizing maps (SOMs) are widely used in several fields of application, from neurobiology to multivariate data analysis. In that context, this paper presents variants of the classic SOM algorithm. With respect to the traditional SOM, the modifications regard the core of the algorithm, (the learning rule), but do not alter the two main tasks it performs, i.e. vector quantization combined with topology preservation. After an intuitive justification based on geometrical considerations, three new rules are defined in addition to the original one. They develop interesting properties such as recursive neighborhood adaptation and non-radial neighborhood adaptation. In order to assess the relative performances and speeds of convergence, the four rules are used to train several maps and the results are compared according to several error measures (quantization error and topology preservation criterions).
自组织映射（SOM）在从神经生物学到多变量数据分析等多个应用领域中得到了广泛应用。在此背景下，本文提出了经典SOM算法的变体。相对于传统的SOM，这些修改涉及算法的核心（学习规则），但不改变其执行的两个主要任务，即结合拓扑保持的矢量量化。在基于几何考虑进行直观论证之后，除了原始规则之外还定义了三个新规则。它们具有诸如递归邻域自适应和非径向邻域自适应等有趣的特性。为了评估相对性能和收敛速度，使用这四个规则训练多个映射，并根据几种误差度量（量化误差和拓扑保持准则）对结果进行比较。
