Learning discriminant isomap for dimensionality reduction

In order to extend the unsupervised nonlinear dimensionality reduction method Isomap for use in supervised learning, a new supervised manifold learning method namely discriminant Isomap (D-Isomap) is proposed, in which the geometrical structure of each class data is preserved by keeping geodesic distances between data points of the same class and the discriminant capacity is enhanced by maximizing the distances between data points of different classes. A new objective function is defined for this purpose and the corresponding optimization problem is solved by using the SMACOF algorithm. The effectiveness of D-Isomap is examined by extensive simulations on artificial and real-world data sets, including MNIST, USPS, and UCI. In both visualization and classification experiments, D-Isomap achieves comparable or better performance than the widely used dimensionality reduction algorithms.