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

- 3 Downloads

## 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

clustering INDCLUS individual partitions three-way proximity data## Notes

### Acknowledgements

The authors are grateful to the Associate Editor and referees for their valuable comments and suggestions which greatly improved the presentation and content of the first version.

## Supplementary material

## References

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