Recombining partitions via unimodality tests

Abstract

In this article we propose a recombination procedure for previously split data. It is basedon the study of modes in the density of the data, since departing from unimodality canbe a sign of the presence of clusters. We develop an algorithm that integrates a splitting process inherited from the SAR algorithm (Peña et al., 2004) with unimodality tests such as the dip test proposed by Hartigan and Hartigan (1985), and finally, we use anetwork configuration to visualize the results. We show that this can be a useful tool to detect heterogeneity in the data, but limited to univariate data because of the nature of the dip test. In a second stage we discuss the use of multivariate mode detection tests to avoid dimensionality reduction techniques such as projecting multivariate data into one dimension. The results of the application of multivariate unimodality tests show that is possible to detect the cluster structure of the data, although more research can be oriented to estimate the proper fine-tuning of some parameters of the test for a given dataset or distribution.