Matrices satisfying regular minimality

Matthias Trendtel; Ali Ünlü; Ehtibar N. Dzhafarov

doi:10.3389/fpsyg.2010.00211

Matrices satisfying regular minimality

Matthias Trendtel, Ali Ünlü, Ehtibar N. Dzhafarov

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

2 Scopus citations

Abstract

A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no tied entries. Under a certain "meta-probabilistic" model this proportion can be interpreted as the probability with which a randomly chosen matrix turns out to be RM-compliant.

Original language	English
Article number	Article 211
Journal	Frontiers in Psychology
Volume	1
Issue number	DEC
DOIs	https://doi.org/10.3389/fpsyg.2010.00211
State	Published - 2010
Externally published	Yes

Keywords

Discriminability
Permutations
Regular minimality

Access to Document

10.3389/fpsyg.2010.00211

Cite this

@article{84d29676bd024334aadf3c0cef9e3420,

title = "Matrices satisfying regular minimality",

abstract = "A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no tied entries. Under a certain {"}meta-probabilistic{"} model this proportion can be interpreted as the probability with which a randomly chosen matrix turns out to be RM-compliant.",

keywords = "Discriminability, Permutations, Regular minimality",

author = "Matthias Trendtel and Ali {\"U}nl{\"u} and Dzhafarov, {Ehtibar N.}",

year = "2010",

doi = "10.3389/fpsyg.2010.00211",

language = "English",

volume = "1",

journal = "Frontiers in Psychology",

issn = "1664-1078",

publisher = "Frontiers Media SA",

number = "DEC",

}

TY - JOUR

T1 - Matrices satisfying regular minimality

AU - Trendtel, Matthias

AU - Ünlü, Ali

AU - Dzhafarov, Ehtibar N.

PY - 2010

Y1 - 2010

N2 - A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no tied entries. Under a certain "meta-probabilistic" model this proportion can be interpreted as the probability with which a randomly chosen matrix turns out to be RM-compliant.

AB - A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no tied entries. Under a certain "meta-probabilistic" model this proportion can be interpreted as the probability with which a randomly chosen matrix turns out to be RM-compliant.

KW - Discriminability

KW - Permutations

KW - Regular minimality

UR - http://www.scopus.com/inward/record.url?scp=79960055485&partnerID=8YFLogxK

U2 - 10.3389/fpsyg.2010.00211

DO - 10.3389/fpsyg.2010.00211

M3 - Article

AN - SCOPUS:79960055485

SN - 1664-1078

VL - 1

JO - Frontiers in Psychology

JF - Frontiers in Psychology

IS - DEC

M1 - Article 211

ER -

Matrices satisfying regular minimality

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this