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We design a distributed function-aware quantization scheme for distributedfunctional compression. We consider $2$ correlated sources $X_1$ and $X_2$ anda destination that seeks an estimate $\hat{f}$ for the outcome of a continuousfunction $f(X_1,\,X_2)$. We develop a compression scheme called hyper binningin order to quantize $f$ via minimizing the entropy of joint sourcepartitioning. Hyper binning is a natural generalization of Cover's random codeconstruction for the asymptotically optimal Slepian-Wolf encoding scheme thatmakes use of orthogonal binning. The key idea behind this approach is to uselinear discriminant analysis in order to characterize different source featurecombinations. This scheme captures the correlation between the sources and thefunction's structure as a means of dimensionality reduction. We investigate theperformance of hyper binning for different source distributions and identifywhich classes of sources entail more partitioning to achieve better functionapproximation. Our approach brings an information theory perspective to thetraditional vector quantization technique from signal processing.

A Distributed Computationally Aware Quantizer Design via Hyper Binning