A generalized optimization of the K-d tree for fast nearest-neighbour search

The problem of efficient optimization of the K-d (K-dimensional) tree for fast nearest-neighbor search under a bucket-Voronoi intersection framework is addressed. A new optimization criterion is proposed which is based on a geometric interpretation of the optimization problem using a direct characterization of the number of Voronoi intersections in the lower and upper regions of a partitioned node as a function of the partition location. The proposed optimization criterion is more efficient than the maximum product criterion (MPC) used recently. The authors give a clear geometric interpretation of the MPC and explain the reasons for its inefficiency. The proposed optimization is used for fast vector quantization encoding of speech and is empirically observed to achieve constant search complexity for O (log N) tree depths