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In this monograph, we study the problem of high-dimensional indexing and systematically introduce two efficient index structures: one for range queries and the other for similarity queries. Extensive experiments and comparison studies are conducted to demonstrate the superiority of the proposed indexing methods. Many new database applications, such as multimedia databases or stock price information systems, transform important features or properties of data objects into high-dimensional points. Searching for objects based on these features is thus a search of points in this feature space. To support efficient retrieval in such high-dimensional databases, indexes are required to prune the search space. Indexes for low-dimensional databases are well studied, whereas most of these application specific indexes are not scaleable with the number of dimensions, and they are not designed to support similarity searches and high-dimensional joins.
A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
In this monograph, we study the problem of high-dimensional indexing and systematically introduce two efficient index structures: one for range queries and the other for similarity queries. Extensive experiments and comparison studies are conducted to demonstrate the superiority of the proposed indexing methods. Many new database applications, such as multimedia databases or stock price information systems, transform important features or properties of data objects into high-dimensional points. Searching for objects based on these features is thus a search of points in this feature space. To support efficient retrieval in such high-dimensional databases, indexes are required to prune the search space. Indexes for low-dimensional databases are well studied, whereas most of these application specific indexes are not scaleable with the number of dimensions, and they are not designed to support similarity searches and high-dimensional joins.
This book constitutes the refereed proceedings of the 8th International Conference on Database Theory, ICDT 2001, held in London, UK, in January 2001. The 26 revised full papers presented together with two invited papers were carefully reviewed and selected from 75 submissions. All current issues on database theory and the foundations of database systems are addressed. Among the topics covered are database queries, SQL, information retrieval, database logic, database mining, constraint databases, transactions, algorithmic aspects, semi-structured data, data engineering, XML, term rewriting, clustering, etc.
Scientific Essay from the year 2015 in the subject Mathematics - Miscellaneous, language: English, abstract: Representation of two dimensional objects into one dimensional space is simple and efficient when using a two coordinate system imposed upon a grid. However, when the two dimensions are expanded far beyond visual and sometimes mental understanding, techniques are used to quantify and simplify the representation of such objects. These techniques center around spatial interpretations by means of a space-filling curve. Since the late 1800's, mathematicians and computer scientists have succeeded with algorithms that express high dimensional geometries. However, very few implementations of the algorithms beyond three dimensions for computing these geometries exist. We propose using the basic spatial computations developed by pioneers in the field like G. Peano, D. Hilbert, E. H. Moore, and others in a working model. The algorithms in this paper are fully implemented in high-level programming languages utilizing a relation database management system. We show the execution speeds of the algorithms using a space-filling curve index for searching compared to brute force searching. Finally, we contrast three space-filling curve algorithms: Moore, Hilbert, and Morton, in execution time of searching for high dimensional data in point queries and range queries.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Fundamentals of Database Indexing and Searching presents well-known database searching and indexing techniques. It focuses on similarity search queries, showing how to use distance functions to measure the notion of dissimilarity. After defining database queries and similarity search queries, the book organizes the most common and representative index structures according to their characteristics. The author first describes low-dimensional index structures, memory-based index structures, and hierarchical disk-based index structures. He then outlines useful distance measures and index structures that use the distance information to efficiently solve similarity search queries. Focusing on the difficult dimensionality phenomenon, he also presents several indexing methods that specifically deal with high-dimensional spaces. In addition, the book covers data reduction techniques, including embedding, various data transforms, and histograms. Through numerous real-world examples, this book explores how to effectively index and search for information in large collections of data. Requiring only a basic computer science background, it is accessible to practitioners and advanced undergraduate students.
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