Polynomial Representation of Classifiers with Independent Discrete-Valued Features

Godfried T. Toussaint

doi:10.1109/TC.1972.5008928

Polynomial Representation of Classifiers with Independent Discrete-Valued Features

Godfried T. Toussaint

Computer Science

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

Abstract

It is shown that for n-valued conditionally independent features a large family of classifiers can be expressed as an (n—list-degree polynomial discriminant function. The usefulness of the polynomial expansion is discussed and demonstrated by considering the first-order Minkowski metric, the Euclidean distance, and Bayes’ classifiers for the ternary-feature case. Finally, some interesting side observations on the classifiers are made with respect to optimality and computational requirements.

Original language	English (US)
Pages (from-to)	205-208
Number of pages	4
Journal	IEEE Transactions on Computers
Volume	C-21
Issue number	2
DOIs	https://doi.org/10.1109/TC.1972.5008928
State	Published - Feb 1972

Keywords

Bayes’
classifier Euclidean distance classifier Minkowski metric classifier polynomial discriminant functions

ASJC Scopus subject areas

Software
Theoretical Computer Science
Hardware and Architecture
Computational Theory and Mathematics

Access to Document

10.1109/TC.1972.5008928

Cite this

@article{0dd55d593f8c45888b51cdebba880ea1,

title = "Polynomial Representation of Classifiers with Independent Discrete-Valued Features",

abstract = "It is shown that for n-valued conditionally independent features a large family of classifiers can be expressed as an (n—list-degree polynomial discriminant function. The usefulness of the polynomial expansion is discussed and demonstrated by considering the first-order Minkowski metric, the Euclidean distance, and Bayes{\textquoteright} classifiers for the ternary-feature case. Finally, some interesting side observations on the classifiers are made with respect to optimality and computational requirements.",

keywords = "Bayes{\textquoteright}, classifier Euclidean distance classifier Minkowski metric classifier polynomial discriminant functions",

author = "Toussaint, {Godfried T.}",

year = "1972",

month = feb,

doi = "10.1109/TC.1972.5008928",

language = "English (US)",

volume = "C-21",

pages = "205--208",

journal = "IEEE Transactions on Computers",

issn = "0018-9340",

publisher = "IEEE Computer Society",

number = "2",

}

TY - JOUR

T1 - Polynomial Representation of Classifiers with Independent Discrete-Valued Features

AU - Toussaint, Godfried T.

PY - 1972/2

Y1 - 1972/2

N2 - It is shown that for n-valued conditionally independent features a large family of classifiers can be expressed as an (n—list-degree polynomial discriminant function. The usefulness of the polynomial expansion is discussed and demonstrated by considering the first-order Minkowski metric, the Euclidean distance, and Bayes’ classifiers for the ternary-feature case. Finally, some interesting side observations on the classifiers are made with respect to optimality and computational requirements.

AB - It is shown that for n-valued conditionally independent features a large family of classifiers can be expressed as an (n—list-degree polynomial discriminant function. The usefulness of the polynomial expansion is discussed and demonstrated by considering the first-order Minkowski metric, the Euclidean distance, and Bayes’ classifiers for the ternary-feature case. Finally, some interesting side observations on the classifiers are made with respect to optimality and computational requirements.

KW - Bayes’

KW - classifier Euclidean distance classifier Minkowski metric classifier polynomial discriminant functions

UR - http://www.scopus.com/inward/record.url?scp=33845276095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845276095&partnerID=8YFLogxK

U2 - 10.1109/TC.1972.5008928

DO - 10.1109/TC.1972.5008928

M3 - Article

AN - SCOPUS:33845276095

SN - 0018-9340

VL - C-21

SP - 205

EP - 208

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

IS - 2

ER -

Polynomial Representation of Classifiers with Independent Discrete-Valued Features

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this