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This paper deals with pattern recognition in a distributed computing context of the peer-to-peer type, that should be more and more interesting for multimedia data indexing and retrieval. Our goal is estimating of class-conditional probability densities, that take the form of Gaussian mixture models (GMM). Originally, we propagate GMMs in a decentralized fashion (gossip) in a network, and aggregate GMMs from various sources, through a technique that only involves little computation and that makes parsimonious usage of the network resource, as model parameters rather than data are transmitted. The aggregation is based on iterative optimization of an approximation of a KL divergence allowing closed-form computation between mixture models. Experimental results demonstrate the scheme to the case of speaker recognition.