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

530 Citations (Scopus)

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

Access to Document

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

Cite this

@article{6a9d932ca6264a2f86f6e11d5db3547c,

title = "Kernels and regularization on graphs",

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.",

author = "Smola, {Alexander J.} and Risi Kondor",

year = "2003",

doi = "10.1007/978-3-540-45167-9_12",

language = "English",

volume = "2777",

pages = "144--158",

journal = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

issn = "0302-9743",

publisher = "Springer Verlag",

note = "16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003 ; Conference date: 24-08-2003 Through 27-08-2003",

}

TY - JOUR

T1 - Kernels and regularization on graphs

AU - Smola, Alexander J.

AU - Kondor, Risi

PY - 2003

Y1 - 2003

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=9444285502&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-45167-9_12

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

M3 - Conference article

AN - SCOPUS:9444285502

SN - 0302-9743

VL - 2777

SP - 144

EP - 158

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

Access to Document

Other files and links

Fingerprint

Cite this