Kernel Isomap on Noisy Manifold

Abstract

In the human brain, it is well known that perception is based on similarity rather than coordinates and it is carried out on the manifold of data set. Isomap (Tenenbaum et al., 2000) is one of widely-used low-dimensional embedding methods where approximate geodesic distance on a weighted graph is used in the framework of classical scaling (metric MDS). In this paper, we consider two critical issues missing in Isomap: (1) generalization property; (2) topological stability and present our robust kernel Isomap method, armed with such two properties. The useful behavior and validity of our robust kernel Isomap, is confirmed through numerical experiments with several data sets including real world data