Foundations of Vector Retrieval

This book presents the fundamentals of vector retrieval. To this end, it delves into important data structures and algorithms that have been successfully used to solve the vector retrieval problem efficiently and effectively.

This monograph is divided into four parts. The first part introduces the problem of vector retrieval and formalizes the concepts involved. The second part delves into retrieval algorithms that help solve the vector retrieval problem efficiently and effectively. It includes a chapter each on brand-and-bound algorithms, locality sensitive hashing, graph algorithms, clustering, and sampling. Part three is devoted to vector compression and comprises chapters on quantization and sketching. Finally, the fourth part presents a review of background material in a series of appendices, summarizing relevant concepts from probability, concentration inequalities, and linear algebra.

The book emphasizes the theoretical aspects of algorithms and presents related theorems and proofs. It is thus mainly written for researchers and graduate students in theoretical computer science and database and information systems who want to learn about the theoretical foundations of vector retrieval.

Table of Contents

Part I Introduction

Chapter 1 Vector Retrieval

Chapter 2 Retrieval Stability in High Dimensions

Chapter 3 Intrinsic Dimensionality

Part II Retrieval Algorithms

Chapter 4 Branch-and-Bound Algorithms

Chapter 5 locality Sensitive Hashing

Chapter 6 Graph Algorithms

Chapter 7 Clustering

Chapter 8 Sampling Algorithms

Part Ill Compression

Chapter 9 Quantization

Chapter 10 Sketching

Part IV Appendices

Appendix A Collections

Appendix B Probability Review

Appendix C Concentration of Measure

Appendix D Linear Algebra Review

About the Author

Sebastian Bruch works at Pinecone in the United States as a research scientist. His research is centered around probabilistic data structures and approximate algorithms for retrieval, and efficient inference algorithms for learnt ranking functions. He is presently serving as an Associate Editor with the ACM TOIS journal.