Query Point Nearest Neighbor

We explore the eeect of dimensionality on the \nearest neigh-bor" problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as di-mensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective , we present empirical results on both real and synthetic data sets that demonstrate that this eeect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this eeect does not occur. However , our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is awed, and should be modiied. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!