  In this paper a variation of the classic vector quantization problem is
considered. In the standard formulation, a quantizer is designed to minimize
the distortion between input and output when the number of reconstruction
points is fixed. We consider, instead, the scenario in which the number of
comparators used in quantization is fixed. More precisely, we study the case in
which a vector quantizer of dimension d is comprised of k comparators, each
receiving a linear combination of the inputs and producing the output value
one/zero if this linear combination is above/below a certain threshold. In
reconstruction, the comparators' output is mapped to a reconstruction point,
chosen so as to minimize a chosen distortion measure between the quantizer
input and its reconstruction. The Comparison-Limited Vector Quantization (CLVQ)
problem is then defined as the problem of optimally designing the configuration
of the compactors and the choice of reconstruction points so as to minimize the
given distortion. In this paper, we design a numerical optimization algorithm
for the CLVQ problem. This algorithm leverages combinatorial geometrical
notions to describe the hyperplane arrangement induced by the configuration of
the comparators. It also relies on a genetic genetic meta heuristic to improve
the selection of the quantizer initialization and avoid local minima
encountered during optimization. We numerically evaluate the performance of our
algorithm in the case of input distributions following uniform and Gaussian
i.i.d. sources to be compressed under quadratic distortion and compare it to
the classic Linde-Buzo-Gray (LBG) algorithm.
