Quantization based nearest-neighbor-preserving metric approximation

To reduce the computational burden of the nearest neighbor search (NNS) problem, most existing algorithms focus on `preprocessing´ the data set to reduce the number of objects to be examined for each querying operation (e.g., efficient data structures, metric space transforms). In this paper we present a quantization based nearest-neighbor-preserving metric approximation algorithm (QNNM) that leads to further complexity reduction by simplifying the metric computation. The proposed algorithm is based on three observations: (i) the query vector is fixed during the entire search process, (ii) the-minimum distance exhibits an extreme value distribution, and (iii) there is high homogeneity of viewpoints. Based on these, QNNM approximates original/benchmark metric in terms of preserving the fidelity of NNS rather than the distance itself, while achieving significantly lower complexity using a query-dependent quantizer. We formulate a quantizer design problem where the goal is to minimize the average NNS error. We show how the query adaptive quantizers can be designed off-line without prior knowledge of the query and present an efficient and specifically tailored off-line optimization algorithm to find such optimal quantizer. Experimental results in a motion estimation (ME) application show minimal performance degradation (average 0.05 dB loss) when using optimized 1-bit quantizer.