Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

Sebastian Fuchs; Fabrizio Durante; F. Marta L.   di Lascio

doi:10.1016/j.csda.2021.107201

Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

Sebastian Fuchs, Fabrizio Durante, F. Marta L. di Lascio

Artificial Intelligence and Human Interfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Peer-reviewed

Abstract

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

Originalsprache	Englisch
Aufsatznummer	107201
Seitenumfang	26
Fachzeitschrift	Computational Statistics and Data Analysis
Jahrgang	159
DOIs	https://doi.org/10.1016/j.csda.2021.107201
Publikationsstatus	Veröffentlicht - 2021

Bibliographische Notiz

Funding Information:
FD has been supported by the project “Stochastic Models for Complex Systems” by Italian MIUR (PRIN 2017, Project no. 2017JFFHSH ). FMLDL has been supported by the project “The use of Copula for the Analysis of Complex and Extreme Energy and Climate data (CACEEC)” by the Free University of Bozen-Bolzano , Faculty of Economics and Management (Grant Nos. WW200S ). SF gratefully acknowledges the support of the WISS 2025 project ’IDA-lab Salzburg’ ( 20204-WISS/225/197-2019 and 0102-F1901166-KZP ).

Publisher Copyright:
© 2021 The Author(s)

Schlagwörter

Comonotonicity
Copula
Cluster analysis
Dissimilarity
Stochastic dependence

Systematik der Wissenschaftszweige 2012

101 Mathematik

Zugriff auf Dokument

10.1016/j.csda.2021.107201Lizenz: CC BY

Andere Dateien und Links

Dieses zitieren

@article{10aad686916743fbb69ca4ce30242726,

title = "Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables",

abstract = "A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.",

keywords = "Comonotonicity, Copula, Cluster analysis, Dissimilarity, Stochastic dependence, Cluster analysis, Comonotonicity, Copula, Dissimilarity, Stochastic dependence",

author = "Sebastian Fuchs and Fabrizio Durante and {di Lascio}, {F. Marta L.}",

note = "Publisher Copyright: {\textcopyright} 2021 The Author(s)",

year = "2021",

doi = "10.1016/j.csda.2021.107201",

language = "English",

volume = "159",

journal = "Computational Statistics and Data Analysis",

issn = "0167-9473",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

AU - Fuchs, Sebastian

AU - Durante, Fabrizio

AU - di Lascio, F. Marta L.

PY - 2021

Y1 - 2021

N2 - A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

AB - A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

KW - Comonotonicity

KW - Copula

KW - Cluster analysis

KW - Dissimilarity

KW - Stochastic dependence

KW - Cluster analysis

KW - Comonotonicity

KW - Copula

KW - Dissimilarity

KW - Stochastic dependence

UR - http://www.scopus.com/inward/record.url?scp=85102056002&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/59d0a2a1-1f77-308e-bbd5-48edf4fdeeb1/

UR - https://resolver.obvsg.at/urn:nbn:at:at-ubs:3-23445

U2 - 10.1016/j.csda.2021.107201

DO - 10.1016/j.csda.2021.107201

M3 - Article

SN - 0167-9473

VL - 159

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

M1 - 107201

ER -