Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-12T22:36:38.660Z Has data issue: false hasContentIssue false
  • English
  • Français

ROOTCLUS: Searching for “ROOT CLUSters” in Three-Way Proximity Data

Published online by Cambridge University Press:  01 January 2025

Laura Bocci and
Donatella VicariOpen the ORCID record for Donatella Vicari[Opens in a new window]
Laura Bocci
Affiliation:
Sapienza University of Rome
Donatella Vicari*
Affiliation:
Sapienza University of Rome
*
Correspondence should be made to Donatella Vicari, Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy. Email:donatella.vicari@uniroma1.it
Get accessRights & Permissions [Opens in a new window]

Abstract

In the context of three-way proximity data, an INDCLUS-type model is presented to address the issue of subject heterogeneity regarding the perception of object pairwise similarity. A model, termed ROOTCLUS, is presented that allows for the detection of a subset of objects whose similarities are described in terms of non-overlapping clusters (ROOT CLUSters) common across all subjects. For the other objects, Individual partitions, which are subject specific, are allowed where clusters are linked one-to-one to the Root clusters. A sound ALS-type algorithm to fit the model to data is presented. The novel method is evaluated in an extensive simulation study and illustrated with empirical data sets.

Keywords

clusteringINDCLUSindividual partitionsthree-way proximity data

Information

Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 4 , December 2019, pp. 941 - 985
Copyright
Copyright © 2019 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-019-09686-1) contains supplementary material, which is available to authorized users.

References

Bocci, L., &Vicari, D.. GINDCLUS: Generalized INDCLUS with external information. Psychometrika, (2017). 82 355– 381. CrossRefGoogle ScholarPubMed
Bocci, L.,Vicari, D., &Vichi, M.. A mixture model for the classification of three-way proximity data. Computational Statistics & Data Analysis, (2006). 50 1625– 1654. CrossRefGoogle Scholar
Calinski, T., &Harabasz, J.. A dendrite method for cluster analysis. Communications in Statistics, (1974). 3 1– 27. CrossRefGoogle Scholar
Carroll, J. D., &Arabie, P.. INDCLUS: An individual differences generalization of ADCLUS model and the MAPCLUS algorithm. Psychometrika, (1983). 48 157– 169. CrossRefGoogle Scholar
Carroll, J. D., &Chang, J. J.. Analysis of individual differences in multidimensional scaling via an N-generalization of the Eckart–Young decomposition. Psychometrika, (1970). 35 283– 319. CrossRefGoogle Scholar
Chaturvedi, A., &Carroll, J. D.. CLUSCALE (CLUstering and multidimensional SCAL[E]ing): A three-way hybrid model incorporating clustering and multidimensional scaling structure. Journal of Classification, (2006). 23 269– 299. CrossRefGoogle Scholar
Chaturvedi, A. J., & Carroll, J. D.. An alternating combinatorial optimization approach to fitting the INDCLUS and generalized INDCLUS models. Journal of Classification, (1994). 11 155– 170. CrossRefGoogle Scholar
Cohen, J.. A coefficient of agreement for nominal scales. Educational and Psychological Measurement, (1960). 20 37– 46. CrossRefGoogle Scholar
De Leeuw, J., Bock, H. H., Lenski, W., & Richter, M. M.. Block-relaxation algorithms in statistics. Information systems and data analysis, (1994). Berlin: Springer. 308– 325. CrossRefGoogle Scholar
Giordani, P., &Kiers, H.A. L.. FINDCLUS: Fuzzy INdividual Differences CLUStering. Journal of Classification, (2012). 29 170– 198. CrossRefGoogle Scholar
Gordon, A. D., &Vichi, M.. Partitions of Partitions. Journal of Classification, (1998). 15 265– 285. CrossRefGoogle Scholar
Hubert, L. J., &Arabie, P.. Comparing partitions. Journal of Classification, (1985). 2 193– 218. CrossRefGoogle Scholar
Hubert, L. J.,Arabie, P., &Meulman, J.. The structural representation of proximity matrices with MATLAB, (2006). Philadelphia: SIAM. CrossRefGoogle Scholar
Kiers, H.A. L.. A modification of the SINDCLUS algorithm for fitting the ADCLUS and INDCLUS models. Journal of Classification, (1997). 14 297– 310. CrossRefGoogle Scholar
Lawson, C. L., & Hanson, R. J.. Solving least squares problems, (1974). Englewood Cliffs: Prentice Hall. Google Scholar
McDonald, R. P.. A simple comprehensive model for the analysis of covariance structures: Some remarks on applications. British Journal of Mathematical and Statistical Psychology, (1980). 33 161– 183. CrossRefGoogle Scholar
Mirkin, B.G.. Additive clustering and qualitative factor analysis methods for similarity matrices. Journal of Classification, (1987). 4 7– 31. CrossRefGoogle Scholar
Rao, C. R., &Mitra, S.. Generalized inverse of matrices and its applications, (1971). New York: Wiley. Google Scholar
Rocci, R., &Vichi, M.. Two-mode multi-partitioning. Computational Statistics & Data Analysis, (2008). 52 1984– 2003. CrossRefGoogle Scholar
Shepard, R. N., &Arabie, P.. Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, (1979). 86 87– 123. CrossRefGoogle Scholar
Schepers, J.,Ceulemans, E., &Van Mechelen, I.. Selecting among multi-mode partitioning models of different complexities: A comparison of four model selection criteria. Journal of Classification, (2008). 25 67– 85. CrossRefGoogle Scholar
Schiffman, S. S.,Reynolds, M. L., &Young, F. W.. Introduction to multidimensional scaling, (1981). London: Academic Press. Google Scholar
Vicari, D., &Vichi, M.. Structural classification analysis of three-way dissimilarity data. Journal of Classification, (2009). 26 121– 154. CrossRefGoogle Scholar
Vichi, M.. One mode classification of a three-way data set. Journal of Classification, (1999). 16 27– 44. CrossRefGoogle Scholar
Wedel, M., &DeSarbo, WS.. Mixtures of (constrained) ultrametric trees. Psychometrika, (1998). 63 419– 443. CrossRefGoogle Scholar
Wilderjans, T. F.,Depril, D., &Van Mechelen, I.. Block-relaxation approaches for fitting the INDCLUS model. Journal of Classification, (2012). 29 277– 296. CrossRefGoogle Scholar
Supplementary material: File

Bocci and Vicari supplementary material

Bocci and Vicari supplementary material
Download Bocci and Vicari supplementary material(File)
File 286.3 KB