The Effects of Dimensionality Curse in High Dimensional kNN Search

The dimensionality curse phenomenon states that in high dimensional spaces distances between nearest and farthest points from query points become almost equal. Therefore, nearest neighbor calculations cannot discriminate candidate points. Many indexing methods that try to cope with the dimensionality curse in high dimensional spaces have been proposed, but, usually these methods end up behaving like the sequential scan over the database in terms of accessed pages when queries like k-Nearest Neighbors are examined. In this paper, we experiment with state of the art multi-attribute indexing methods and try to investigate when these methods reach their limits, namely, at what dimensionality a kNN query requires visiting all the data pages. In our experiments we compare the Hybrid Tree, the R*-tree, and, the iDistance Method.