Natural Nearest Neighbor for Isomap Algorithm without Free-Parameter

Abstract

Isomapis a classic and efficient manifold learning algorithm, which aims at finding the intrinsic structure hidden in high dimensional data. Only deficiency appeared in this algorithm is that it requires user to input a free parameterkwhich is closely related to the success of unfolding the true intrinsic structure and the algorithm’s topological stability. Here, we propose a novel and simplek-nn basedconcept: natural nearest neighbor (3N), which is independent of parameterk, so as to addressing the longstanding problem of how to automatically choosing the only free parameterkin manifold learning algorithms so far, and implementing completely unsupervised learning algorithm3N-Isomapfor nonlinear dimensionality reduction without the use of any priori information about the intrinsic structure. Experiment results show that3N-Isomapis a more practical and simple algorithm thanIsomap.