We propose an infinite mixture model for the clustering of positive data. The proposed model is based on the generalized inverted Dirichlet distribution which has a more general covariance structure than the inverted Dirichlet that has been widely used recently in several machine learning and data mining applications. The proposed mixture is developed in an elegant way that allows simultaneous clustering and feature selection, and is learned using a fully Bayesian approach via Gibbs sampling. The merits of the proposed approach are demonstrated using a challenging application namely images categorization.