ASNN: Accelerated Searching for Natural Neighbors

Abstract

How to set k value for k-nearest neighbors is a primary problem in machine learning, pattern recognition and knowledge discovery. Natural neighbor (NaN) is an adaptive neighbor concept for solving this problem, which combines k-nearest neighbors and reverse k-nearest neighbors to adaptively obtain k value. It has been proven effective in clustering analysis, classification and outlier detection. However, the existing algorithms for searching NaN all use a global search strategy, which increases unnecessary consumption of time on non-critical points. In this paper, we propose a novel accelerated algorithm for searching natural neighbor, called ASNN. It is based on the fact that if the remote objects have NaNs, others certainly have the NaNs. The main idea of ASNN is that it first extracts remote points, then only searches the neighbors of remote points, instead of all points, so that ASNN can quickly obtain the natural neighbor eigenvalue (NaNE). To identify the remote objects, ASNN only searches the 1-nearest neighbor for each object with kd-tree, so its time complexity is reduced to $\boldsymbol{O(nlogn)}$ from $\boldsymbol{O(n^2)}$, and the local search strategy makes it run faster than the existing algorithms. To illustrate the efficiency of ASNN, we compare it with three existing algorithms NaNs, kd-NaN and FSNN. The experiments on synthetic and real datasets tell that ASNN runs much faster than NaNs, kd-NaN and FSNN, especially for datasets with large scale.