Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples

@article{belkin06manifold, abstract = {We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases. We use properties of reproducing kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely graph-based approaches) we obtain a natural out-of-sample extension to novel examples and so are able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semi-supervised algorithms are able to use unlabeled data effectively. Finally we have a brief discussion of unsupervised and fully supervised learning within our general framework.}, author = {Belkin, Mikhail and Niyogi, Partha and Sindhwani, Vikas }, citeulike-article-id = {2095902}, journal = {Journal of Machine Learning Research}, keywords = {manifolds, semisupervised}, month = {November}, pages = {2399--2434}, posted-at = {2007-12-11 22:49:03}, priority = {2}, title = {Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples}, url = {http://www.jmlr.org/papers/volume7/belkin06a/belkin06a.pdf}, volume = {7}, year = {2006} }

TY - JOUR ID - belkin06manifold L3 - citeulike-article-id:2095902 TI - Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples JF - Journal of Machine Learning Research VL - 7 SP - 2399 EP - 2434 N2 - We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases. We use properties of reproducing kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely graph-based approaches) we obtain a natural out-of-sample extension to novel examples and so are able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semi-supervised algorithms are able to use unlabeled data effectively. Finally we have a brief discussion of unsupervised and fully supervised learning within our general framework. KW - manifolds KW - semisupervised AU - Belkin, Mikhail AU - Niyogi, Partha AU - Sindhwani, Vikas PY - 2006/11// UR - http://www.jmlr.org/papers/volume7/belkin06a/belkin06a.pdf ER -