Face Recognition Using Hierarchical Isomap

Nonlinear dimension reduction method Isomap has demonstrated promising performance in finding low dimensional manifolds from data points in the high dimensional input space. The Isomap method estimates geodesic distance between data points instead of taking the Euclidean distance and then uses multidimensional scaling (MDS) to induce a low dimensional embedding from the geodesic distance graph. However, since the original prototype Isomap does not discriminate data acquired from different classes, when concerned with multi-class data, several isolated sub-graphs will result in undesirable embedding. In this paper, a hierarchical Isomap algorithm is proposed for the multi-class data, which first computes within-class and between-class geodesic distances separately and the final embedding is obtained from the augmented geodesic distance matrix using MDS. The experimental results reveal a promising performance of the proposed algorithm.