A Depth-first Adaptive KNN Searching Algorithm

Given n data points in d-dimensional space, k nearest neighbors searching involves determining k nearest of these data points to a given query point. A depth-first adaptive kNN searching (DAKNNs) algorithm is proposed. The algorithm finds k nearest neighbors of the query point in a small hyperball in order to improve the efficiencies. It firstly determines the minimal radius r
min
of the hyperball according to the rules, and then estimates the effective radius r
effective
of other points' hyperball. With the algorithm, the cost to find k nearest neighbors of one point is O(ad)(1≤ a ≪n), and the cost of preprocessing is O(dnlog
2
n). Our experiment shows the algorithm performance is superior to other known algorithms.