K-Nearest Neighbor Search using the Pyramid Technique

A k-nearest neighbor search algorithm for the Pyramid technique is presented. The Pyramid technique divides d-dimensional data space into 2d pyramids. Given a query point q, we initialize the radius of a range query to be the furthest distance of the k candidate nearest neighbors from q in the pyramid which q is in, then examine the rest of the pyramids one by one. After one pyramid is checked, the radius of the range query decreases or remains the same. We compared the knearest neighbor performance of the Pyramid technique with the k-d tree, the R∗-tree and naive search. Experimental results show that our decreasing radius Pyramid k-nearest neighbor search algorithm is efficient when d ≤ log2 n.