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GINDCLUS: Generalized INDCLUS with External Information

Published online by Cambridge University Press:  01 January 2025

Laura Bocci  and
Donatella Vicari Open 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
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Abstract

A Generalized INDCLUS model, termed GINDCLUS, is presented for clustering three-way two-mode proximity data. In order to account for the heterogeneity of the data, both a partition of the subjects into homogeneous classes and a covering of the objects into groups are simultaneously determined. Furthermore, the availability of information which is external to the three-way data is exploited to better account for such heterogeneity: the weights of both classifications are linearly linked to external variables allowing for the identification of meaningful classes of subjects and groups of objects. The model is fitted in a least-squares framework, and an efficient Alternating Least-Squares algorithm is provided. An extensive simulation study and an application on benchmark data are also presented.

Keywords

clusteringexternal informationINDCLUSthree-way proximity data

Information

Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 2 , June 2017 , pp. 355 - 381
Copyright
Copyright © 2016 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-016-9526-9) contains supplementary material, which is available to authorized users.

References

Bach, F., & Jenatton, R., & Mairal, J., & Obozinski, G. Sra, S., & Nowozin, S., & Wright, S. J. (2011). Convex optimization with sparsity-inducing norms. Optimization for machine learning, Cambridge: MIT Press.Google Scholar
Bocci, L., & Vicari, D., & Vichi, M. (2006). A mixture model for the classification of three-way proximity data. Computational Statistics & Data Analysis, 50, 1625–1654CrossRefGoogle Scholar
Bocci, L., & Vichi, M. (2011). The K-INDSCAL model for heterogeneous three-way dissimilarity data. Psychometrika, 76, 691–714CrossRefGoogle ScholarPubMed
Bock, H. H. Bozdogan, H., & Gupta, A. K. (1987). On the interface between cluster analysis, principal component analysis, and multidimensional scaling. Multivariate statistical modeling and data analysis, New York: Reidel 17–34CrossRefGoogle Scholar
Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling. Theory and application, Berlin: Springer.Google Scholar
Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3, 1–27.CrossRefGoogle Scholar
Carroll, J. D., & Arabie, P. (1983). INDCLUS: An individual differences generalization of ADCLUS model and the MAPCLUS algorithm. Psychometrika, 48, 157–169CrossRefGoogle Scholar
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46CrossRefGoogle Scholar
Gill, P. E., & Murray, W., & Wright, M. H. (1981). Practical optimization, London: Academic Press.Google Scholar
Giordani, P., & Kiers, H. A. L. (2012). FINDCLUS: Fuzzy INdividual Differences CLUStering. Journal of Classification, 29, 170–198CrossRefGoogle Scholar
Gordon, A. D., & Vichi, M. (1998). Partitions of partitions. Journal of Classification, 15, 265–285CrossRefGoogle Scholar
Heiser, W. J. Opitz, O., & Lausen Klar, O. (1993). Clustering in low-dimensional space. Information and classification: Concepts, methods and applications, Berlin: Springer.Google Scholar
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193–218.CrossRefGoogle Scholar
Hubert, L. J., & Arabie, P., & Meulman, J. (2006). The structural representation of proximity matrices with MATLAB, Philadelphia: SIAMCrossRefGoogle Scholar
Kiers, H. A. L., & Vicari, V., & Vichi, M. (2005). Simultaneous classification and multidimensional scaling with external information. Psychometrika, 70, 433–460CrossRefGoogle Scholar
Lawson, C. L., & Hanson, R. J. (1974). Solving least squares problems, Englewood Cliffs: Prentice Hall.Google Scholar
McDonald, R. P. (1980). A simple comprehensive model for the analysis of covariance structures: Some remarks on applications. British Journal of Mathematical and Statistical Psychology, 33, 161–183CrossRefGoogle Scholar
Rao, C. R., & Mitra, S. (1971). Generalized inverse of matrices and its applications, New York: Wiley.Google Scholar
Schiffman, S. S., & Reynolds, M. L., & Young, F. W. (1981). Introduction to multidimensional scaling, London: Academic Press.Google Scholar
Shepard, R. N., & Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87–123CrossRefGoogle Scholar
Ten Berge, J. M. F., & Kiers, H. A. L. (2005). A comparison of two methods for fitting the INDCLUS model. Journal of Classification, 22, 273–286CrossRefGoogle Scholar
Vicari, D., & Vichi, M. (2009). Structural classification analysis of three-way dissimilarity data. Journal of Classification, 26, 121–154CrossRefGoogle Scholar
Wedel, M., & DeSarbo, W. S. (1998). Mixtures of (constrained) ultrametric trees. Psychometrika, 63, 419–443CrossRefGoogle Scholar
Wilderjans, T. F., & Depril, D., & Van Mechelen, I. (2012). Block-relaxation approaches for fitting the INDCLUS model. Journal of Classification, 29, 277–296CrossRefGoogle Scholar
Winsberg, S., & De Soete, G. (1993). A latent class approach to fitting the weighted Euclidean model, CLASCAL. Psychometrika, 58, 315–330CrossRefGoogle Scholar
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