  We design a distributed function-aware quantization scheme for distributed
functional compression. We consider $2$ correlated sources $X_1$ and $X_2$ and
a destination that seeks an estimate $\hat{f}$ for the outcome of a continuous
function $f(X_1,\,X_2)$. We develop a compression scheme called hyper binning
in order to quantize $f$ via minimizing the entropy of joint source
partitioning. Hyper binning is a natural generalization of Cover's random code
construction for the asymptotically optimal Slepian-Wolf encoding scheme that
makes use of orthogonal binning. The key idea behind this approach is to use
linear discriminant analysis in order to characterize different source feature
combinations. This scheme captures the correlation between the sources and the
function's structure as a means of dimensionality reduction. We investigate the
performance of hyper binning for different source distributions and identify
which classes of sources entail more partitioning to achieve better function
approximation. Our approach brings an information theory perspective to the
traditional vector quantization technique from signal processing.
