New variant of ISOMAP for imperfect manifold

Abstract

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.