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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Article
A Topological Clustering of Variables
Author(s)
Rafik Abdesselam
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DOI:10.17265/2159-5291/2021.02.001
Affiliation(s)
ERIC and COACTIS Laboratories, Department of Economics and Management, University of Lyon, France
ABSTRACT
The clustering of objects (individuals or variables) is one of the mostused approaches to exploring multivariate data. The two most common unsupervised clustering strategies are hierarchical ascending clustering (HAC) and k-meanspartitioning used to identify groups of similar objects in a dataset to divide it intohomogeneous groups.The proposed topological clustering of variables, called TCV, studies an homogeneous set of variables defined on the same set of individuals, based on the notionof neighborhood graphs, some of these variables are more-or-less correlated or linkedaccording to the type quantitative or qualitative of the variables. This topologicaldata analysis approach can then be useful for dimension reduction and variable selection. It’s a topological hierarchical clustering analysis of a set of variables which canbe quantitative, qualitative or a mixture of both. It arranges variables into homogeneous groups according to their correlations or associations studied in a topologicalcontext of principal component analysis (PCA) or multiple correspondence analysis(MCA). The proposed TCV is adapted to the type of data considered, its principleis presented and illustrated using simple real datasets with quantitative, qualitativeand mixed variables. The results of these illustrative examples are compared to those of other variables clustering approaches.
KEYWORDS
Hierarchical clustering, proximity measure, neighborhood graph, adjacency matrix, multivariate quantitative, qualitative and mixed data analysis, dimension reduction.
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