A new approach to cluster analysis: the clustering-function-based method

The purpose of this paper is to present a new statistical approach to hierarchical cluster analysis with n objects measured on p variables. Motivated by the model of multivariate analysis of variance and the method of maximum likelihood, a clustering problem is formulated as a least squares optimisation problem, simultaneously solving for both an n-vector of unknown group membership of objects and a linear clustering function. This formulation is shown to be linked to linear regression analysis and Fisher linear discriminant analysis and includes principalcomponent regression for tackling multicollinearity or rank-deficiency, polynomial or B-splines regression for handling non-linearity, and various variable selection methods to eliminate redundant variables from data analysis. Algorithmic issues are investigated using sign eigenanalysis.