An extended ISOMAP by enhancing similarity for clustering

Abstract

Isomap is an important dimension reduction method for clustering data with relatively large features. Isomap uses geodesic distance instead of Euclidean distance to reflect geometry of the underlying manifold, while it ignores the classification principle that the distance between samples on different manifolds should be large and the distance between samples on the same manifold should be small. In this paper, we employed a path based distance to extend Isomap for clustering. The path based distance measure strengthens the similarity of the points on the same manifold. The useful behavior of the similarity strengthening Isomap is confirmed through numerical experiments with several data sets. © 2012 Springer-Verlag.