Manifold learning

A manifold is a topological space which is locally Euclidean.

manifold based semi-supervised learning

Geometricallymotivated approaches to data analysis in high dimensionalspaces have been shown to be effective in discovering thegeometrical structure of the underlying manifold.Examples include ISOAMP [Tenenbaum etal., 2000], Laplacian Eigenmap [Belkin and Niyogi, 2001],Locally Linear Embedding [Roweis and Saul, 2000].However,they are unsupervised in nature and fail to discover the discriminantstructure in the data. In the meantime, manifold based semi-supervised learning has attracted considerable attention[Zhou et al., 2003], [Belkin et al., 2004]. Thesemethodsmake use of both labeled and unlabeled samples. The labeledsamples are used to discover the discriminant structure,while the unlabeled samples are used to discover the geometricalstructure.