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Approximate nearest neighbor (ANN) search is a fundamental problem in manyareas of data mining, machine learning and computer vision. The performance oftraditional hierarchical structure (tree) based methods decreases as thedimensionality of data grows, while hashing based methods usually lackefficiency in practice. Recently, the graph based methods have drawnconsiderable attention. The main idea is that \emph{a neighbor of a neighbor isalso likely to be a neighbor}, which we refer as \emph{NN-expansion}. Thesemethods construct a $k$-nearest neighbor ($k$NN) graph offline. And at onlinesearch stage, these methods find candidate neighbors of a query point in someway (\eg, random selection), and then check the neighbors of these candidateneighbors for closer ones iteratively. Despite some promising results, thereare mainly two problems with these approaches: 1) These approaches tend toconverge to local optima. 2) Constructing a $k$NN graph is time consuming. Wefind that these two problems can be nicely solved when we provide a goodinitialization for NN-expansion. In this paper, we propose EFANNA, an extremelyfast approximate nearest neighbor search algorithm based on $k$NN Graph. Efannanicely combines the advantages of hierarchical structure based methods andnearest-neighbor-graph based methods. Extensive experiments have shown thatEFANNA outperforms the state-of-art algorithms both on approximate nearestneighbor search and approximate nearest neighbor graph construction. To thebest of our knowledge, EFANNA is the fastest algorithm so far both onapproximate nearest neighbor graph construction and approximate nearestneighbor search. A library EFANNA based on this research is released on Github.

EFANNA : An Extremely Fast Approximate Nearest Neighbor Search Algorithm Based on kNN Graph