Chromatic nearest neighbor searching: A query sensitive approach

The nearest neighbor problem is that of preprocessing a set P of n data points in Rd 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 ≥ 1, the problem is to determine the color occurring most frequently among the k nearest neighbors. The chromatic version of the nearest neighbor problem is used in many applications in pattern recognition and learning. In this paper we present a simple algorithm for solving the chromatic 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 ε ≥ 0, and consider the same problem in the context of approximate nearest neighbor searching. We present empirical evidence that for well clustered data sets, this approach leads to significant improvements in efficiency. Key words: Chromatic nearest neighbors, classification algorithms, pattern recognition, multidimensional searching, BBD trees, branch and bound search, query sensitive analysis.