Abnormal structure in regular data revealed by Isomap with natural nearest neighbor

Abstract

Isomap is a classical and efficient manifold learning algorithm, which aims at finding the intrinsic structure hidden in high dimensional data. One deficiency appeared in this algorithm is that it requires user to input a free parameter k, but by applying natural nearest neighbor instead of k-nn or ε-nn to the original Isomap (called 3N-Isomap), this problem can be easily solved. In this paper, we demonstrate another feature of 3N-Isomap that can be used to discover abnormality information within regular data set by combining the natural nearest neighborhood graph and the estimation of geodesic distance upon this graph. Experiment results based on same regular data sets show that 3N-Isomap has the ability to discover abnormal structure hidden in high-dimensional data set. © 2011 Springer-Verlag Berlin Heidelberg.