On cluster analysis of complex and heterogeneous data

Abstract

Cluster analysis or "unsupervised" classification (from "unsupervised learning", in pattern recognition literature) usually concerns a set of exploratory multivariate data analysis methods and techniques for grouping either statistical data units or variables into groups of similar elements, that is finding a clustering structure in the data. Classical clustering methods usually work with a set of objects as statistical data units described by a set of homogeneous (that is, of the same type) variables in a two-way framework. This paradigm can be extended in such way that data units may be either simple / first-order elements (e.g., objects, subjects, cases) or groups of / second-order or more elements from a population (e.g., subsets, samples, classes of a partition) and/or descriptive variables may simultaneously be of different (e.g., binary, multi-valued, histogram or interval) types. Therefore, one has a complex and/or heterogeneous data set under analysis. In that case classification will often be carried out by using a three-way or a symbolic/complex approach. The present work synthesizes previous methodological results and shows several developments mostly regarding hierarchical cluster analysis of complex data, where statistical data units are described by either a homogeneous or a heterogeneous set of variables. We will illustrate that approach on a case study issued from the statistical literature. The methodology has been applied with success in a data mining context, concerning multivariate analysis of real-life data bases from economy, management, medicine, education and social sciences.