Fast $k$-NNG construction with GPU-based quick multi-select

In this paper we describe a new brute force algorithm for building the $k$-Nearest Neighbor Graph ($k$-NNG). The $k$-NNG algorithm has many applications in areas such as machine learning, bio-informatics, and clustering analysis. While there are very efficient algorithms for data of low dimensions, for high dimensional data the brute force search is the best algorithm. There are two main parts to the algorithm: the first part is finding the distances between the input vectors which may be formulated as a matrix multiplication problem. The second is the selection of the $k$-NNs for each of the query vectors. For the second part, we describe a novel graphics processing unit (GPU) -based multi-select algorithm based on quick sort. Our optimization makes clever use of warp voting functions available on the latest GPUs along with use-controlled cache. Benchmarks show significant improvement over state-of-the-art implementations of the $k$-NN search on GPUs.