The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies.
Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges.
The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data.
Jeremy Kepner is an MIT Lincoln Laboratory Fellow, Founder and Head of the MIT Lincoln Laboratory Supercomputing Center, and Research Affiliate in MIT's Mathematics Department.
Hayden Jananthan is a PhD candidate in the Department of Mathematics at Vanderbilt University.
Charles E. Leiserson is Edwin Sibley Webster Professor in Electrical Engineering and Computer Science at MIT.
Mathematics of Big Data presents a sophisticated view of matrices, graphs, databases, and spreadsheets, with many examples to help the discussion. The authors present the topic in three parts—applications and practice, mathematical foundations, and linear systems—with self-contained chapters to allow for easy reference and browsing. The algorithms are expressed in D4M, with execution possible in Matlab, Octave, and Julia. With exercises at the end of each section, the book can be used as a supplemental or primary text for a class on big data, algorithms, data structures, data analytics, linear algebra, or abstract algebra.
Jack Dongarra, Professor, University of Tennessee, Oak Ridge National Laboratory, and University of Manchester; coauthor of MPI: The Complete Reference, second edition, volume 1
In this era of big data, new methods for gaining insights promise to improve all aspects of our lives. This new textbook from Kepner and Jananthan is a fantastic resource for data scientists to understand the unifying mathematics for big data problems that covers everything from databases to graph analytics.
David A. Bader, Professor and Chair, School of Computational Science and Engineering, Georgia Institute of Technology