An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

Ronald L Breiger, Scott A. Boorman, Phipps Arabie

Research output: Contribution to journalArticle

413 Citations (Scopus)

Abstract

A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [-111-1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.

Original languageEnglish (US)
Pages (from-to)328-383
Number of pages56
JournalJournal of Mathematical Psychology
Volume12
Issue number3
DOIs
StatePublished - 1975
Externally publishedYes

Fingerprint

Social Network Analysis
Electric network analysis
Social Support
Cluster Analysis
Clustering
Scaling
Hierarchical Clustering
INDSCAL
Product-moment correlation
Square matrix
Convergence Properties
Social Networks
Converge
Alternatives

ASJC Scopus subject areas

  • Applied Mathematics
  • Experimental and Cognitive Psychology

Cite this

An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling. / Breiger, Ronald L; Boorman, Scott A.; Arabie, Phipps.

In: Journal of Mathematical Psychology, Vol. 12, No. 3, 1975, p. 328-383.

Research output: Contribution to journalArticle

@article{df16e117d7504dad85fb3718d70a85ef,
title = "An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling",
abstract = "A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [-111-1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.",
author = "Breiger, {Ronald L} and Boorman, {Scott A.} and Phipps Arabie",
year = "1975",
doi = "10.1016/0022-2496(75)90028-0",
language = "English (US)",
volume = "12",
pages = "328--383",
journal = "Journal of Mathematical Psychology",
issn = "0022-2496",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - An algorithm for clustering relational data with applications to social network analysis and comparison with multidimensional scaling

AU - Breiger, Ronald L

AU - Boorman, Scott A.

AU - Arabie, Phipps

PY - 1975

Y1 - 1975

N2 - A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [-111-1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.

AB - A method of hierarchical clustering for relational data is presented, which begins by forming a new square matrix of product-moment correlations between the columns (or rows) of the original data (represented as an n × m matrix). Iterative application of this simple procedure will in general converge to a matrix that may be permuted into the blocked form [-111-1]. This convergence property may be used as the basis of an algorithm (CONCOR) for hierarchical clustering. The CONCOR procedure is applied to several illustrative sets of social network data and is found to give results that are highly compatible with analyses and interpretations of the same data using the blockmodel approach of White (White, Boorman & Breiger, 1976). The results using CONCOR are then compared with results obtained using alternative methods of clustering and scaling (MDSCAL, INDSCAL, HICLUS, ADCLUS) on the same data sets.

UR - http://www.scopus.com/inward/record.url?scp=49549145171&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549145171&partnerID=8YFLogxK

U2 - 10.1016/0022-2496(75)90028-0

DO - 10.1016/0022-2496(75)90028-0

M3 - Article

AN - SCOPUS:49549145171

VL - 12

SP - 328

EP - 383

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

IS - 3

ER -