Chromatic nearest neighbor searching: A query sensitive approach

The nearest neighbor problem is that of preprocessing a set P of n data poi nts in R-d so that given any query point q, the closest point in P to q can be determined efficiently. In the chromatic nearest neighbor problem, each point of P is assigned a color, and the problem is to determine the color of the nearest point to the query point. More generally, given k greater th an or equal to 1, the problem is to determine the color occurring most freq uently among the k nearest neighbors. The chromatic version of the nearest neighbor problem is used in many applications in pattern recognition and le arning. In this paper we present a simple algorithm for solving the chromat ic k nearest neighbor problem. We provide a query sensitive analysis, which shows that if the color classes form spatially well separated clusters (as often happens in practice), then queries can be answered quite efficiently . We also allow the user to specify an error bound epsilon greater than or equal to 0, and consider the same problem in the context of approximate nea rest neighbor searching. We present empirical evidence that for well cluste red data sets, this approach leads to significant improvements in efficienc y. (C) 2000 Elsevier Science B.V. All rights reserved.