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We describe a generalization of the multiple-instance learning model in which a bag’s label is not based on a single instance’s proximity to a single target point. Rather, a bag is positive if and only if it contains a collection of instances, each near one of a set of target points. We list potential applications of this model (robot vision, content-based image retrieval, protein sequence identification, and drug discovery) and describe target concepts for these applications that cannot be represented in the conventional multiple-instance learning model. We then adapt a learning-theoretic algorithm for learning in this model and present empirical results.