A fast nearest neighbor search algorithm by nonlinear embedding

We propose an efficient algorithm to find the exact nearest neighbor based on the Euclidean distance for large-scale computer vision problems. We embed data points nonlinearly onto a low-dimensional space by simple computations and prove that the distance between two points in the embedded space is bounded by the distance in the original space. Instead of computing the distances in the high-dimensional original space to find the nearest neighbor, a lot of candidates are to be rejected based on the distances in the low-dimensional embedded space; due to this property, our algorithm is well-suited for high-dimensional and large-scale problems. We also show that our algorithm is improved further by partitioning input vectors recursively. Contrary to most of existing fast nearest neighbor search algorithms, our technique reports the exact nearest neighbor - not an approximate one - and requires a very simple preprocessing with no sophisticated data structures. We provide the theoretical analysis of our algorithm and evaluate its performance in synthetic and real data.