文献类型：期刊文献

英文题名：Extension of ISOMAP for Imperfect Manifolds

作者：Shao, Chao[1];Hu, Haitao[1]

第一作者：邵超

通讯作者：Shao, C[1]

机构：[1]Henan Univ Econ & Law, Sch Comp & Informat Engn, Zhengzhou, Henan, Peoples R China

第一机构：河南财经政法大学计算机与信息工程学院

通讯机构：[1]corresponding author), Henan Univ Econ & Law, Sch Comp & Informat Engn, Zhengzhou, Henan, Peoples R China.|[1048412]河南财经政法大学计算机与信息工程学院;[10484]河南财经政法大学;

年份：2012

卷号：7

期号：7

起止页码：1780-1785

外文期刊名：JOURNAL OF COMPUTERS

收录：EI(收录号：20123215307854);Scopus(收录号：2-s2.0-84864425595);WOS:【ESCI(收录号:WOS:000218124500029)】；

基金：This work was supported in part by the Research Programme of Henan Fundamental and Advanced Technology of China (No. 112300410201), and the Key Technologies R&D Programme of Henan Province, China (No. 102102210400, 112102310519).

语种：英文

外文关键词：ISOMAP; EN-ISOMAP; EN-MDS; imperfect manifolds; geodesic distance; shortest path distance

摘要：As one of the most promising nonlinear dimensionality reduction techniques, Isometric Mapping (ISOMAP) performs well only when the data belong to a single well-sampled manifold, where geodesic distances can be well approximated by the corresponding shortest path distances in a suitable neighborhood graph. Unfortunately, the approximation gets less and less precise generally as the number of edges of the corresponding shortest path increases, which makes ISOMAP tend to overlap or overcluster the data, especially for disjoint or imperfect manifolds. To alleviate this problem, this paper presented a variant of ISOMAP, i.e. Edge Number-based ISOMAP (ENISOMAP), which uses a new variant of Multidimensional Scaling (MDS), i.e. Edge Number-based Multidimensional Scaling (EN-MDS), instead of the classical Multidimensional Scaling (CMDS) to map the data into the low-dimensional embedding space. As a nonlinear variant of MDS, ENMDS gives larger weight to the distances with fewer edges, which are generally better approximated and then more trustworthy than those with more edges, and thus can preserve the more trustworthy distances more precisely. Finally, experimental results verify that not only imperfect manifolds but also intrinsically curved manifold can be visualized by EN-ISOMAP well.