Supervised Isomap with Explicit Mapping

Isomap is one of the recently proposed manifold learning algorithms for nonlinear dimensionality reduction. However, Isomap not only suffers from a deficiency of no explicit mapping function, which is from high dimensional space to low dimensional space, but also does not employ the class information. In this paper, a supervised version of Isomap with explicit mapping, called SE-Isomap, is proposed. In SEIsomap, geodesic distance matrix is calculated with respect to the class label information and Multidimensional Scaling (MDS) with explicit transformation is adopted instead of classical MDS used in Isomap. Thanks to the existence of explicit mapping and the use of class label information, SEIsomap can be more easily used in pattern recognition than the original ones. Experimental results on two benchmark data sets demonstrated the performance of the presented method.