Semi-supervised Riemannian Dimensionality Reduction and Classification Using a Manifold-based Random Walker Graph

Efficient classification of manifold-based data demands dimensionality reduction. However, the optimal lower dimension is mostly unknown. Also, supervised classification demands a collection of expert-annotated samples. This collection is tedious, costly, and error prone. Thus, semi-supervised classifications are motivated. In this paper, we propose a principled method to determine the optimal lower dimension and to reduce dimension of manifold-based data for their semi-supervised classification. This method relies on a manifold-based random walker graph and enhances the discriminative power of the classifier in the reduced dimensional space. The reduced dimensional data can be classified by any method or the same graph after adapting edge weights of the graph to them. Thus, the proposed dimensionality reduction is independent of the classifier type. This method is evaluated on segmenting tissues on fat-water (2-channel) magnetic resonance images.