Learning the Kernel Matrix with Semi-Definite Programming

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Learning the Kernel Matrix with Semi-Definite Programming (2002)

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by Gert R. G. Lanckriet , Nello Cristianini , Laurent El Ghaoui , Peter Bartlett , Michael I. Jordan

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764 - 21 self

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@MISC{Lanckriet02learningthe,
    author = {Gert R. G. Lanckriet and Nello Cristianini and Laurent El Ghaoui and Peter Bartlett and Michael I. Jordan},
    title = {Learning the Kernel Matrix with Semi-Definite Programming },
    year = {2002}
}

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Abstract

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space---classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied

Keyphrases

kernel matrix data point algorithm work linear relation machine learning inner product embedding space relative position so-called kernel matrix semi-definite programming positive definite matrix euclidean space

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