Extended isomap for pattern classification

Abstract

The Isomap method has demonstrated promising results in finding low dimensional manifolds from data points in the high dimensional input space. While classical subspace methods use Euclidean or Manhattan metrics to represent distances between data points and apply Principal Component Analysis to induce linear manifolds, the Isomap method estimates geodesic distances between data points and then uses Multi-Dimensional Scaling to induce low dimensional manifolds. Since the Isomap method is developed based on reconstruction principle, it may not be optimal from the classification viewpoint. In this paper, we present an extended Isomap method that utilizes Fisher Linear Discriminant for pattern classification. Numerous experiments on image data sets show that our extension is more effective than the original Isomap method for pattern classification. Furthermore, the extended Isomap method shows promising results compared with best methods in the face recognition literature.