Manifold regularization: A geometric framework for learning from labeled and unlabeled examples

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Manifold regularization: A geometric framework for learning from labeled and unlabeled examples (2006)

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by Mikhail Belkin , Partha Niyogi , Vikas Sindhwani

Venue:	JOURNAL OF MACHINE LEARNING RESEARCH
Citations:	576 - 16 self

BibTeX

@TECHREPORT{Belkin06manifoldregularization:,
    author = {Mikhail Belkin and Partha Niyogi and Vikas Sindhwani},
    title = {Manifold regularization: A geometric framework for learning from labeled and unlabeled examples},
    institution = {JOURNAL OF MACHINE LEARNING RESEARCH},
    year = {2006}
}

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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.

Keyphrases

manifold regularization geometric framework unlabeled example general-purpose learner semi-supervised framework special case new form theoretical basis regularized least square general framework graph-based approach unlabeled data present experimental evidence semi-supervised setting semi-supervised algorithm brief discussion transductive graph utilize property standard method marginal distribution natural out-of-sample extension support vector machine kernel hilbert space new representer

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