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 0.05dB loss) when using optimized 1-bit quantizer.