Modal clustering on PPGMMGA projection subspace

PPGMMGA is a projection pursuit (PP) algorithm aimed at detecting and visualising clustering structures in multivariate data. The algorithm uses the negentropy as PP index obtained by fitting Gaussian mixture models (GMMs) for density estimation and, then, exploits genetic algorithms (GAs) for its optimisation. Since the PPGMMGA algorithm is a dimension reduction technique specifically introduced for visualisation purposes, cluster memberships are not explicitly provided. In this paper a modal clustering approach is proposed for estimating clusters of projected data points. In particular, a modal EM algorithm is employed to estimate the modes corresponding to the local maxima in the projection subspace of the underlying density estimated using parsimonious GMMs. Data points are then clustered according to the domain of attraction of the identified modes. Simulated and real data are discussed to illustrate the proposed method and evaluate the clustering performance.