Manifold-based approaches for improved classification

While manifold structure is often exploited for dimensionality reduction or feature extraction, this structure is rarely used by classification algorithms. We present a class of algorithms that utilize the low-dimensional manifold nature of signal ensembles and result in improved classification performance. The algorithms are built within theoretical frameworks that take into consideration prior knowledge of geometric structure in both labeled and unlabeled data points. Additionally, these frameworks can exploit recent results on random projections of smooth manifolds to ensure computational feasibility on extremely high-dimensional problems.