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
N1 - Funding Information:
’ We are indebted to Harrison White and Paul Levitt for detailed and productive comments, and also to William Batchelder, Paul Holland, J. Clyde Mitchell, Ingram Olkin, Joel Levine, Frederick Mosteller, Joseph Schwartz, and Roger Shepard. Paul Levitt generously gave assistance in surmounting difficulties with a packaged APL version of the Hungarian method for optimal assignment. Together with Breiger, Schwartz codiscovered the mathematical convergence fact on which the CONCOR algorithm rests; he also has contributed many valuable ideas and comments, in particular the approach to simultaneous treatment of multiple relations. We also thank S. F. Sampson for allowing us to cite data and interpretation from his unpublished study, Crisis in a Cloister. Support for the present research was obtained through NSF Grant GS-2689 (Co-principal Investigators: Harrison White and Scott A. Boorman), NIMH Grant MH 21747 (Principal Investigator: Richard C. Atkinson), and funds from Graduate School of the University of Minnesota. Reprint requests should be addressed to: Phipps Arabie, Department Hall, University of Minnesota, Minneapolis, MN 55455.
PY - 1975/8
Y1 - 1975/8
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.
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U2 - 10.1016/0022-2496(75)90028-0
DO - 10.1016/0022-2496(75)90028-0
M3 - Article
AN - SCOPUS:49549145171
SN - 0022-2496
VL - 12
SP - 328
EP - 383
JO - Journal of Mathematical Psychology
JF - Journal of Mathematical Psychology
IS - 3
ER -