Abstract
AbstractA novel clustering model, CPclus, for three-way data concerning a set of objects on which variables are measured by different subjects is proposed. The main aim of the proposal is to simultaneously summarize the objects through clusters and both variables and subjects through components. The object clusters are found by adopting a K-means-based strategy where the centroids are reduced according to the Candecomp/Parafac model in order to exploit the three-way structure of the data. The clustering process is carried out in order to reveal between-cluster differences in mean. Least-squares fitting is performed by using an iterative alternating least-squares algorithm. Model selection is addressed by considering an elbow-based method. An extensive simulation study and some real-life applications show the effectiveness of the proposal, also in comparison with its potential competitors.
Funder
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
Subject
Library and Information Sciences,Statistics, Probability and Uncertainty,Psychology (miscellaneous),Mathematics (miscellaneous)
Reference35 articles.
1. Cariou, V., & Wilderjans, T. F. (2018). Consumer segmentation in multi-attribute product evaluation by means of non-negatively constrained CLV3W. Food Quality and Preference, 67, 18–26.
2. Cariou, V., Alexandre-Gouabau, M. C., & Wilderjans, T. F. (2021). Three-way clustering around latent variables approach with constraints on the configurations to facilitate interpretation. Journal of Chemometrics., 35, e3269.
3. Carroll, J. D., & Chaturvedi, A. (1995). A general approach to clustering and multidimensional scaling of two-way, three-way or higher-way data. In: Luce, D. R. et al. (Eds.), Geometric Representations of perceptual phenomena (pp. 295–318). Mahwah, NJ: Lawrence Erlbaum.
4. Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika, 35, 283–319.
5. De Soete, G., & Carroll, J. D. (1994). k-means clustering in a low-dimensional Euclidean space. In: Diday, E., Lechevallier, Y., Schader, M., Bertrand, P., & Burtschy, B. (Eds.), New Approaches in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization (pp. 212–219). Berlin, Heidelberg: Springer.