应用于不完整流形的ISOMAP算法

摘要

等距特征映射(ISOMAP)算法要求数据位于单一流形之上且具有良好采样,而当数据采样于一个不完整流形时,该算法将会产生“过聚类”问题.为此,提出了一种改进算法-WISOMAP,它采用多维尺度分析(MDS)算法的一个变种-WMDS来降低逼近精度相对较差的多边测地距离在MDS距离保持中的主导作用,使逼近精度相对较好的少边测地距离能够得到更好的保持,从而能在一定程度上缓解“过聚类”问题.实验结果表明WISOMAP算法能更好地对采样于不完整流形的数据进行可视化.%Isometric Feature Mapping (ISOMAP) requires that the data belong to a single well-sampled manifold; however, when the data are sampled from an imperfect manifold, ISOMAP tends to overcluster the data. To alleviate this problem, this paper presented a new variant of ISOMAP called Weighted ISOMAP (WISOMAP), which used Weighted Multidimensional Scaling (WMDS) instead of Classical Multidimensional Scaling ( CMDS) to map the data into the low-dimensional embedding space. As a new variant of MDS, WMDS gave smaller weight to the distances with more edges, which were generally worse approximated and then less trustworthy than those with fewer edges, and thus could limit the effects of the generally worse-approximated distances with many edges and preserved the more trustworthy distances with few edges in the low-dimensional embedding space more precisely, by which the data relying on an imperfect manifold could be visualized better. The efficiency of WISOMAP is verified by experimental results well.