Manifold regularization: A geometric framework for learning from examples

Manifold regularization: A geometric framework for learning from examples (2004)

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by Mikhail Belkin , Partha Niyogi , Vikas Sindhwani , Peter Bartlett

Venue:	Journal of Machine Learning Research
Citations:	197 - 12 self

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Datum	Value	Source
TITLE	Manifold regularization: A geometric framework for learning from examples	INFERENCE
AUTHOR NAME	Mikhail Belkin	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of Computer Science and Engineering; The Ohio State University	SVM HeaderParse 0.2
AUTHOR ADDR	2015 Neil Avenue, Dreese Labs 597; Columbus, OH 43210, USA	SVM HeaderParse 0.2
AUTHOR NAME	Partha Niyogi	SVM HeaderParse 0.2
AUTHOR AFFIL	Departments of Computer Science and Statistics; University of Chicago	SVM HeaderParse 0.2
AUTHOR ADDR	1100 E. 58th Street; Chicago, IL 60637, USA	SVM HeaderParse 0.2
AUTHOR NAME	Vikas Sindhwani	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of Computer Science; University of Chicago	SVM HeaderParse 0.2
AUTHOR ADDR	1100 E. 58th Street; Chicago, IL 60637, USA	SVM HeaderParse 0.2
AUTHOR NAME	Peter Bartlett	SVM HeaderParse 0.2
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 utilize 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. 1.	SVM HeaderParse 0.2
YEAR	2004	INFERENCE
VENUE	Journal of Machine Learning Research	INFERENCE
VENUE TYPE	TECHREPORT	INFERENCE
PAGES	2006	INFERENCE
VOLUME	7	INFERENCE
TECH	Technical Report TR-2004-06	INFERENCE
CITATIONS	54 found	ParsCit 1.0