Extended Isomap for classification

Abstract

The Isomap method has demonstrated promising results in finding a low dimensional embedding from samples in the high dimensional input space. The crux of this method is to estimate geodesic distance with multidimensional scaling for dimensionality reduction. Since the Isomap method is developed based on the reconstruction principle, it may not be optimal from the classification viewpoint. We present an extended Isomap method that utilizes the 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 shows promising results compared with best classification methods in the literature.