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G. Pichler, P. Piantanida, G. Matz:
"Distributed Information-Theoretic Clustering";
IEEE Transactions on Information Theory, 0 (2018).

We study a novel multi-terminal source coding setup motivated by the biclustering problem. Two separate encoders observe two i.i.d. sources Xⁿ and Zⁿ, respectively. The goal is to find rate-limited encodings f(xⁿ) and g(zⁿ) that maximize the mutual information I(f(Xⁿ); g(Zⁿ))/n. We provide inner and outer bounds on the achievable region and discuss connections of this problem with hypothesis testing against independence, pattern recognition, the information bottleneck method, and lossy source coding with logarithmic-loss distortion. Improving previous cardinality bounds allows us to thoroughly study the special case of a binary symmetric source and to quantify the gap between the inner and the outer bound in this special case. Furthermore, we generalize our results to the case of more than two i.i.d. sources. As a special case of this generalization we investigate a multiple description (MD) extension of the CEO problem with log-loss distortion. Surprisingly, this MD-CEO problem permits a tight single-letter characterization of the achievable region.

Source coding; Mutual information; Information bottleneck; CEO problem; Logarithmic loss