A unifying criterion for unsupervised clustering and feature selection

Exploratory data analysis methods are essential for getting insight into data. Identifying the most important variables and detecting quasi-homogenous groups of data are problems of interest in this context. Solving such problems is a difficult task, mainly due to the unsupervised nature of the underlying learning process. Unsupervised feature selection and unsupervised clustering can be successfully approached as optimization problems by means of global optimization heuristics if an appropriate objective function is considered. This paper introduces an objective function capable of efficiently guiding the search for significant features and simultaneously for the respective optimal partitions. Experiments conducted on complex synthetic data suggest that the function we propose is unbiased with respect to both the number of clusters and the number of features.