Kernels and regularization on graphs

Alexander J. Smola; Risi Kondor

doi:10.1007/978-3-540-45167-9_12

Kernels and regularization on graphs

Alexander J. Smola^*, Risi Kondor

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

558 Citations (SciVal)

Abstract

We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.

Original language	English
Pages (from-to)	144-158
Number of pages	15
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2777
DOIs	https://doi.org/10.1007/978-3-540-45167-9_12
Publication status	Published - 2003
Event	16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003 - Washington, DC, United States Duration: 24 Aug 2003 → 27 Aug 2003

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10.1007/978-3-540-45167-9_12

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abstract = "We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.",

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AB - We introduce a family of kernels on graphs based on the notion of regularization operators. This generalizes in a natural way the notion of regularization and Greens functions, as commonly used for real valued functions, to graphs. It turns out that diffusion kernels can be found as a special case of our reasoning. We show that the class of positive, monotonically decreasing functions on the unit interval leads to kernels and corresponding regularization operators.

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DO - 10.1007/978-3-540-45167-9_12

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JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003

Y2 - 24 August 2003 through 27 August 2003

ER -

Kernels and regularization on graphs

Abstract

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