Semi-Supervised Learning on Riemannian Manifolds

摘要: We consider the general problem of utilizing both labeled and unlabeled data to improve classification accuracy. Under assumption that lie on a submanifold in high dimensional space, we develop an algorithmic framework classify partially set principled manner. The central idea our approach is functions are naturally defined only question rather than total ambient space. Using Laplace-Beltrami operator one produces basis (the Laplacian Eigenmaps) for Hilbert space square integrable submanifold. To recover such basis, examples required. Once obtained, training can be performed using set. Our algorithm models manifold adjacency graph approximates by Laplacian. provide details algorithm, its theoretical justification, several practical applications image, speech, text classification.