Minimax distance metric-based neighborhood selection algorithm for Isomap

Isomap (Isometric feature mapping) is one of recently proposed nonlinear dimensionality reduction algorithm, where geodesic distances between points are extracted instead of simply taking the Euclidean distance. Neighborhood size (number of nearest neighbors k or neighborhood radius ε) is a key parameter of Isomap algorithm, which has to be specified manually. If the chosen neighborhood size of data points is not appropriate, the neighborhood of these data points will include data points from other branches of the manifold, which can severely impair its topological stability and performance. In this paper, an improved Isomap algorithm, the so-called MDM-Isomap (Minimax Distance Metric-based neighborhood selection algorithm for Isomap) is introduced to acquire a suitable neighborhood size for Isomap. Experimental results show that MDM-Isomap has been verified by face manifold learning and classification experimental results very well.