iDistance

Abstract: The R-tree, one of the most popular access methods for rectangles, is based on the heuristic optimization of the area of the enclosing rectangle in each inner node. By running numerous experiments in a standardized testbed under highly varying data, queries and operations, we were able to design the R*-tree which incorporates a combined optimization of area, margin and overlap of each enclosing rectangle in the directory. Using our standardized testbed in an exhaustive performance comparison, it turned out that the R*-tree clearly outperforms the existing R-tree variants. Guttman's linear and quadratic R-tree and Greene's variant of the R-tree. This superiority of the R*-tree holds for different types of queries and operations, such as map overlay, for both rectangles and multidimensional points in all experiments. From a practical point of view the R*-tree is very attractive because of the following two reasons 1 it efficiently supports point and spatial data at the same time and 2 its implementation cost is only slightly higher than that of other R-trees.

Abstract: A new access method, called M-tree, is proposed to organize and search large data sets from a generic “metric space”, i.e. where object proximity is only defined by a distance function satisfying the positivity, symmetry, and triangle inequality postulates. We detail algorithms for insertion of objects and split management, which keep the M-tree always balanced - several heuristic split alternatives are considered and experimentally evaluated. Algorithms for similarity (range and k-nearest neighbors) queries are also described. Results from extensive experimentation with a prototype system are reported, considering as the performance criteria the number of page I/O’s and the number of distance computations. The results demonstrate that the Mtree indeed extends the domain of applicability beyond the traditional vector spaces, performs reasonably well in high-dimensional data spaces, and scales well in case of growing files.

Abstract: Efficient indexing of high dimensional feature vectors is important to allow visual information systems and a number other applications to scale up to large databases. We define this problem as "similarity indexing" and describe the fundamental types of "similarity queries" that we believe should be supported. We also propose a new dynamic structure for similarity indexing called the similarity search tree or SS-tree. In nearly every test we performed on high dimensional data, we found that this structure performed better than the R*-tree. Our tests also show that the SS-tree is much better suited for approximate queries than the R*-tree.

Abstract: In this article, we present an efficient Bp-tree based indexing method, called iDistance, for K-nearest neighbor (KNN) search in a high-dimensional metric space. iDistance partitions the data based on a space- or data-partitioning strategy, and selects a reference point for each partition. The data points in each partition are transformed into a single dimensional value based on their similarity with respect to the reference point. This allows the points to be indexed using a Bp-tree structure and KNN search to be performed using one-dimensional range search. The choice of partition and reference points adapts the index structure to the data distribution.We conducted extensive experiments to evaluate the iDistance technique, and report results demonstrating its effectiveness. We also present a cost model for iDistance KNN search, which can be exploited in query optimization.