Abstract: Multidimensional similarity join finds pairs of multi-dimensional points that are within some small distance of each other. Databases in domains such as multimedia and time-series can require a high number of dimensions. The .epsilon.-k-d-B tree has been proposed as a data structure that scales better as number of dimensions increases compared to previous data structures such as the R-tree (and variations), grid-file, and k-d-B tree. We present a cost model of the .epsilon.-k-d-B tree and use it to optimize the leaf size. This new leaf size is shown to be better in most situations compared to previous work that used a constant leaf size. We present novel parallel procedures for the .epsilon.-k-d-B tree. A load-balancing strategy based on equi-depth histograms is shown to work well for uniform or low-skew situations, whereas another based on weighted, equi-depth histograms works far better for high-skew datasets. The latter strategy is only slightly slower than the former strategy for low skew datasets.

Abstract: The present invention is directed to an improved data clustering method and apparatus for use in data mining operations. The present invention determines the pattern vectors of a k-d tree structure which are closest to a given prototype cluster by pruning prototypes through geometrical constraints, before a k-means process is applied to the prototypes. For each sub-branch in the k-d tree, a candidate set of prototypes is formed from the parent of a child node. The minimum and maximum distances from any point in the child node to any prototype in the candidate set is determined. The smallest of the maximum distances found is compared to the minimum distances of each prototype in the candidate set. Those prototypes with a minimum distance greater than the smallest of the maximum distances are pruned or eliminated. Pruning the number of remote prototypes reduces the number of distance calculations for the k-means process, significantly reducing the overall computation time.