Название: Mathematics of Big dаta: Spreadsheets, Databases, Matrices, and Graphs
Автор: Jeremy Kepner, Hayden Jananthan
Издательство: The MIT Press
Год: 2018
Страниц: 490
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

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.

While most algorithms are presented mathematically, when working code examples are required, these are expressed in D4M. The D4M software package is an open-source toolbox that runs in the MATLAB, GNU Octave, and Julia programming languages. D4M is the first practical implementation of associative array mathematics and has been used in diverse applications. D4M has a complete set of documentation, example programs, tutorial slides, and many hours of instructional videos that are all available online. The D4M examples in the book are written in MATLAB, and some familiarity with MATLAB is helpful.