In this paper, we concern ourselves with the problem of simultaneous positive data clustering and feature selection. We propose a statistical framework based on finite mixture models of generalized inverted Dirichlet (GID) distributions. The GID offers a more practical and flexible alternative to the inverted Dirichlet which has a very restrictive covariance structure. For learning the parameters of the resulting mixture, we propose an approach based on minimum message length (MML) criterion. We use synthetic data and real data generated from a challenging application that concerns objects detection to demonstrate the feasibility and advantages of the proposed method.