Fast exact k nearest neighbors search using an orthogonal search tree

The problem of k nearest neighbors (kNN) is to find the nearest k neighbors for a query point from a given data set. In this paper, a novel fast kNN search method using an orthogonal search tree is proposed. The proposed method creates an orthogonal search tree for a data set using an orthonormal basis evaluated from the data set. To find the kNN for a query point from the data set, projection values of the query point onto orthogonal vectors in the orthonormal basis and a node elimination inequality are applied for pruning unlikely nodes. For a node, which cannot be deleted, a point elimination inequality is further used to reject impossible data points. Experimental results show that the proposed method has good performance on finding kNN for query points and always requires less computation time than available kNN search algorithms, especially for a data set with a big number of data points or a large standard deviation.