Quantize and Conquer: A Dimensionality-Recursive Solution to Clustering, Vector Quantization, and Image Retrieval

Inspired by the close relation between nearest neighbor search and clustering in high-dimensional spaces as well as the success of one helping to solve the other, we introduce a new paradigm where both problems are solved simultaneously. Our solution is recursive, not in the size of input data but in the number of dimensions. One result is a clustering algorithm that is tuned to small codebooks but does not need all data in memory at the same time and is practically constant in the data size. As a by-product, a tree structure performs either exact or approximate quantization on trained centroids, the latter being not very precise but extremely fast. A lesser contribution is a new indexing scheme for image retrieval that exploits multiple small codebooks to provide an arbitrarily fine partition of the descriptor space. Large scale experiments on public datasets exhibit state of the art performance and remarkable generalization.