Dimensionality reduction based on Isomap and Mutual Information Maximization

In dimensionality reduction, Isometric Mapping (Isomap) is a classical method with non-linear feature transform, but relies on minimum matrix distance function and assumptions. Maximization of Mutual Information (MMI) derives the effective dimensionality reduction transform from the Information Theory, but difficult to get the solution. We present a new method (ISO-MMI) for learning discriminative feature transforms, using mutual information between objective function and transformed feature, based on the Isomap algorithms, by complementary combination of these two methods. Numerous experiments on different data sets comparing with PCA, LDA, and Isomap, show the effectiveness of this proposed algorithm.