Geometrical properties of Nu support vector machines with different norms

Kazushi Ikeda; Noboru Murata

doi:10.1162/0899766054796897

Geometrical properties of Nu support vector machines with different norms

Kazushi Ikeda^*, Noboru Murata

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

By employing the L₁ or L_∞ norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L₂ norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the L_p norm is investigated, and the SVM solutions are shown to have rather little dependency on p.

Original language	English
Pages (from-to)	2508-2529
Number of pages	22
Journal	Neural Computation
Volume	17
Issue number	11
DOIs	https://doi.org/10.1162/0899766054796897
Publication status	Published - 2005 Nov 1

ASJC Scopus subject areas

Arts and Humanities (miscellaneous)
Cognitive Neuroscience

Access to Document

10.1162/0899766054796897

Cite this

@article{1f710f07c4e746aaa45eca9cacf6e7f7,

title = "Geometrical properties of Nu support vector machines with different norms",

abstract = "By employing the L1 or L∞ norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L2 norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the Lp norm is investigated, and the SVM solutions are shown to have rather little dependency on p.",

author = "Kazushi Ikeda and Noboru Murata",

year = "2005",

month = nov,

day = "1",

doi = "10.1162/0899766054796897",

language = "English",

volume = "17",

pages = "2508--2529",

journal = "Neural Computation",

issn = "0899-7667",

publisher = "MIT Press Journals",

number = "11",

}

TY - JOUR

T1 - Geometrical properties of Nu support vector machines with different norms

AU - Ikeda, Kazushi

AU - Murata, Noboru

PY - 2005/11/1

Y1 - 2005/11/1

N2 - By employing the L1 or L∞ norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L2 norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the Lp norm is investigated, and the SVM solutions are shown to have rather little dependency on p.

AB - By employing the L1 or L∞ norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L2 norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the Lp norm is investigated, and the SVM solutions are shown to have rather little dependency on p.

UR - http://www.scopus.com/inward/record.url?scp=25144470140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25144470140&partnerID=8YFLogxK

U2 - 10.1162/0899766054796897

DO - 10.1162/0899766054796897

M3 - Article

C2 - 16156937

AN - SCOPUS:25144470140

SN - 0899-7667

VL - 17

SP - 2508

EP - 2529

JO - Neural Computation

JF - Neural Computation

IS - 11

ER -

Geometrical properties of Nu support vector machines with different norms

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this