The similarity join is an important database primitive which has been successfully applied to speed up applications such as similarity search, data analysis and data mining. The similarity join combines two point sets of a multidimensional vector space such that the result contains all point pairs where the distance does not exceed a parameter ε. In this paper, we propose the Epsilon Grid Order, a new algorithm for determining the similarity join of very large data sets. Our solution is based on a particular sort order of the data points, which is obtained by laying an equi-distant grid with cell length ε over the data space and comparing the grid cells lexicographically. A typical problem of grid-based approaches such as MSJ or the ε-kdB-tree is that large portions of the data sets must be held simultaneously in main memory. Therefore, these approaches do not scale to large data sets. Our technique avoids this problem by an external sorting algorithm and a particular scheduling strategy during the join phase. In the experimental evaluation, a substantial improvement over competitive techniques is shown.

Metric databases are databases where a metric distance function is defined for pairs of database objects. In such databases, similarity queries in the form of range queries or k-nearest-neighbor queries are the most important query types. In traditional query processing, single queries are issued independently by different users. In many data mining applications, however, the database is typically explored by iteratively asking similarity queries for answers of previous similarity queries. We introduce a generic scheme for such data mining algorithms and we investigate two orthogonal approaches, reducing I/O cost as well as CPU cost, to speed-up the processing of multiple similarity queries. The proposed techniques apply to any type of similarity query and to an implementation based on an index or using a sequential scan. Parallelization yields an additional impressive speed-up. An extensive performance evaluation confirms the efficiency of our approach.

A broad class of algorithms for knowledge discovery in databases (KDD) relies heavily on similarity queries, i.e. range queries or nearest neighbor queries, in multidimensional feature spaces. Many KDD algorithms perform a similarity query for each point stored in the database. This approach causes serious performance degenerations if the considered data set does not fit into main memory. Usual cache strategies such as LRU fail because the locality of KDD algorithms is typically not high enough. In this paper, we propose to replace repeated similarity queries by the similarity join, a database primitive prevalent in multimedia database systems. We present a schema to transform query intensive KDD algorithms into a representation using the similarity join as a basic operation without affecting the correctness of the result of the considered algorithm. In order to perform a comprehensive experimental evaluation of our approach, we apply the proposed transformation to the clustering algor...

Metric databases are databases where a metric distance function is defined for pairs of database objects. In such databases, similarity queries in the form of range queries or k-nearest neighbor queries are the most important queries. In traditional query processing, single queries are issued independently by different users. In many data mining applications, however, the database is typically explored by iteratively asking similarity queries for answers of previous similarity queries. In this paper, we introduce a generic scheme for such data mining algorithms and we investigate two orthogonal approaches, reducing I/O cost as well as CPU cost, to speed-up the processing of multiple similarity queries. The proposed techniques apply to any type of similarity query and to an implementation based on an index or using a sequential scan. Parallelization yields an additional impressive speed-up. An extensive performance evaluation confirms the efficiency of our approach.

Most similarity search techniques map the data objects into some high-dimensional feature space. The similarity search then corresponds to a nearest-neighbor search in the feature space which is computationally very intensive. In this paper, we present a new parallel method for fast nearest-neighbor search in high-dimensional feature spaces. The core problem of designing a parallel nearest-neighbor algorithm is to find an adequate distribution of the data onto the disks. Unfortunately, the known declustering methods to not perform well for high-dimensional nearest-neighbor search. In contrast, our method has been optimized based on the special properties of high-dimensional spaces and therefore provides a near-optimal distribution of the data items among the disks. The basic idea of our data declustering technique is to assign the buckets corresponding to different quadrants of the data space to different disks. We show that our technique - in contrast to other declustering methods - guarantees that all buckets corresponding to neighboring quadrants are assigned to different disks. We evaluate our method using large amounts of real data (up to 40 MBytes) and compare it with the best known data declustering method, the Hilbert curve. Our experiments show that our method provides an almost linear speed-up and a constant scale-up. Additionally, it outperforms the Hilbert approach by a factor of up to 5.