Applications of average geodesic distance in manifold learning

Abstract

Manifold learning has become a hot issue in the research fields of machine learning and data mining. Current manifold learning algorithms assume that the observed data set has the high density. But, how to evaluate the denseness of the high dimensional observed data set? This paper proposes an algorithm based on the average geodesic distance as the preprocessing step of manifold learning. Moreover, for a high dense data set evaluated, we further utilize the average geodesic distance to quantitatively analyze the mapping relationship between the high-dimensional manifold and the corresponding intrinsic low-dimensional manifold in the known ISOMAP algorithm. Finally, experimental results on two synthetic Swiss-roll data sets show that our method is feasible. © 2008 Springer-Verlag Berlin Heidelberg.