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.

The indexing of high-dimensional data remains a challenging task amidst an active and storied area of computer science research that impacts many far-reaching applications. At the crossroads of databases and machine learning, modern data indexing enables information retrieval capabilities that would otherwise be impractical or near impossible to attain and apply. One such useful retrieval task in our increasingly data-driven world is the k-nearest neighbor (k-NN) search, which returns the k most similar items in a dataset to the search query provided. While the k-NN concept was popularized in every-day use through the sorted (ranked) results of online text-based search engines like Google, multimedia applications are rapidly becoming the new frontier of research. This dissertation advances the current state of high-dimensional data indexing with the creation of a novel index named ID* (\ID Star"). Based on extensive theoretical and empirical analyses, we discuss important challenges associated with high dimensional data and identify several shortcomings of existing indexing approaches and methodologies. By further mitigating against the negative effects of the curse of dimensionality, we are able to push the boundary of effective k-NN retrieval to a higher number of dimensions over much larger volumes of data. As the foundations of the ID* index, we developed an open-source and extensible distance-based indexing framework predicated on the basic concepts of the popular iDistance index, which utilizes an internal B+-tree for efficient one-dimensional data indexing. Through the addition of several new heuristic-guided algorithmic improvements and hybrid indexing extensions, we show that our new ID* index can perform significantly better than several other popular alternative indexing techniques over a wide variety of synthetic and real-world data. In addition, we present applications of our ID* index through the use of k-NN queries in Content-Based Image Retrieval (CBIR) systems and machine learning classification. An emphasis is placed on the NASA sponsored interdisciplinary research goal of developing a CBIR system for large-scale solar image repositories. Since such applications rely on fast and effective k-NN queries over increasingly large-scale and high-dimensional datasets, it is imperative to utilize an efficient data indexing strategy such as the ID* index.

Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

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.