index structure

In this paper, we propose a new method for indexing large amounts of point and spatial data in high-dimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures is the overlap of the bounding boxes in the directory, which increases with growing dimension. To avoid this problem, we introduce a new organization of the directory which uses a split algorithm minimizing overlap and additionally utilizes the concept of supernodes. The basic idea of overlap-minimizing split and supernodes is to keep the directory as hierarchical as possible, and at the same time to avoid splits in the directory that would result in high overlap. Our experiments show that for high-dimensional data, the X-tree outperforms the well-known R*-tree and the TV-tree by up to two orders of magnitude.

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 M-tree 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.

We present an efficient indexing method to locate subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of boxes in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. More detailed, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails in sub-trails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times.