An extended Isomap algorithm for learning multi-class manifold

Isomap is a recently proposed algorithm for manifold learning and nonlinear dimensionality reduction. In the Isomap algorithm, geodesic distances between points are extracted instead of simply taking the Euclidean distance, thus a geometric distance graph is constructed and the embedding is obtained from the graph. However, when this method is applied into multi-class data, several isolated sub-graphs will form thus desirable embedding cannot be achieved. An extended Isomap algorithm is proposed for the multi-class manifold learning which computes within-class and between-class geodesic distances separately and the final embedding is obtained from the augmented geodesic distance matrix using multidimensional scaling algorithm. Experimental results on synthetic and real data reveal the promising performance of the proposed method.