K-nearest neighbor search and outlier detection via minimax distances

Abstract

We study Minimax distance measures for K-nearest neighbor search and classification. Recently, the use of this distance measure is shown to improve the K-nearest neighbor classification results. We consider the computational aspects of this problem and propose an efficient and general-purpose algorithm for computing Minimax neighbors which requires a significantly lower runtime and is applicable with any arbitrary distance measure. We study the computational optimality of our approach and its connection to the Prim's algorithm, and then, generalize our analysis to computing one-to-all Minimax distances. In the following, we investigate in detail the edges selected by Minimax distances and thereby explore the ability of Minimax distances in detecting outlier objects. We evaluate the performance of our methods on a variety of real-world datasets, e.g. text documents and images.