Yin Hujun
Department of Electrical Engineering and Electronics, UMIST, Manchester, UK.
Neural Netw. 2002 Oct-Nov;15(8-9):1005-16. doi: 10.1016/s0893-6080(02)00075-8.
The self-organising map (SOM) has been successfully employed as a nonparametric method for dimensionality reduction and data visualisation. However, for visualisation the SOM requires a colouring scheme to imprint the distances between neurons so that the clustering and boundaries can be seen. Even though the distributions of the data and structures of the clusters are not faithfully portrayed on the map. Recently an extended SOM, called the visualisation-induced SOM (ViSOM) has been proposed to directly preserve the distance information on the map, along with the topology. The ViSOM constrains the lateral contraction forces between neurons and hence regularises the interneuron distances so that distances between neurons in the data space are in proportion to those in the map space. This paper shows that it produces a smooth and graded mesh in the data space and captures the nonlinear manifold of the data. The relationships between the ViSOM and the principal curve/surface are analysed. The ViSOM represents a discrete principal curve or surface and is a natural algorithm for obtaining principal curves/surfaces. Guidelines for applying the ViSOM constraint and setting the resolution parameter are also provided, together with experimental results and comparisons with the SOM, Sammon mapping and principal curve methods.
自组织映射(SOM)已成功用作降维和数据可视化的非参数方法。然而,为了进行可视化,SOM需要一种着色方案来体现神经元之间的距离,以便能够看到聚类和边界。即便数据的分布和聚类结构在映射图上并未得到如实呈现。最近,一种扩展的SOM,即可视化诱导SOM(ViSOM)被提出来,它能在保留拓扑结构的同时,直接在映射图上保留距离信息。ViSOM对神经元之间的横向收缩力进行约束,从而规范神经元间的距离,使得数据空间中神经元之间的距离与映射图空间中的距离成比例。本文表明,它在数据空间中生成了一个平滑且渐变的网格,并捕捉到了数据的非线性流形。分析了ViSOM与主曲线/主曲面之间的关系。ViSOM代表一条离散的主曲线或主曲面,是获取主曲线/主曲面的一种自然算法。还提供了应用ViSOM约束和设置分辨率参数的指导方针,以及实验结果,并与SOM、 Sammon映射和主曲线方法进行了比较。