Selection of the optimal parameter value for the Isomap algorithm

The isometric feature mapping (Isomap) method has demonstrated promising results in finding low-dimensional manifolds from data points in high-dimensional input space. Isomap has one free parameter (number of nearest neighbours K or neighbourhood radius ϵ), which has to be specified manually. In this paper we present a new method for selecting the optimal parameter value for Isomap automatically. Numerous experiments on synthetic and real data sets show the effectiveness of our method.