Linear Discriminant Hierarchical Clustering (LDHC): a modeling and cross-validable divisive clustering method

A simple modification of the linear discriminant classification tree (LDCT) (R. Todeschini and E. Marengo, Linear discriminant classification trees, Chemometrics and Intelligent Laboratory Systems, 16 (1992) 25-35) method is used to deal with clustering problems in the framework of a divisive hierarchical strategy. The method produces a mathematical model which allows the validation of the obtained clusters by using a cross-validation technique; simple parameters can then be estimated to assess the significance of the clusters. The performance of linear discriminant hierarchical clustering has been tested on seven data sets where the class assignments are known