A Fast Nearest-Neighbor Algorithm Based on a Principal Axis Search Tree

A new fast nearest neighbor algorithm is described that uses principal component analysis to build an efficient search tree. At each node in the tree, the data set is partitioned along the direction of maximum variance. The search algorithm efficiently uses a depth-first search and a new elimination criterion. The new algorithm was compared to sixteen other fast nearest neighbor algorithms on three types of common benchmark data sets including problems from time series prediction and image vector quantization. This comparative study illustrates the strengths and weaknesses of all of the leading algorithms. The new algorithm performed very well on all of the data sets and was consistently ranked among the top three algorithms. Keywords— Nearest Neighbor, Vector Quantization Encoding, Principal Components Analysis, Closest Point, Intrinsic Dimension, Post Office Problem