Mathematics of Big Data
Mathematics of Big Data: Spreadsheets, Databases, Matrices, and Graphs
Jeremy Kepner (MIT) and Hayden Jananthan (Vanderbilt)
This book will be available from MIT Press in 2017
In the meantime, please see the related MIT Open Course Ware (OCW) class with many code examples:
Signal Processing on Databases
Table of Contents
Preface
Part I: Applications and Practice
Chapter 1: Introduction and Overview
Chapter 2: Perspectives on Data
Chapter 3: Dynamic Distributed Dimensional Data Model
Chapter 4: Associative Arrays and Musical Metadata
Chapter 5: Associative Arrays and Abstract Art
Chapter 6: Manipulating Graphs with Matrices
Chapter 7: Graph Analysis and Machine Learning Systems
Part II: Mathematical Foundations
Chapter 8: Visualizing the Algebra of Associative Arrays
Chapter 9: Defining the Algebra of Associative Arrays
Chapter 10: Structural Properties of Associative Arrays
Chapter 11: Graph Construction and Graphical Patterns
Chapter 12: Survey of Common Transformations
Part III: Linear Systems
Chapter 13: Maps and Bases
Chapter 14: Linearity of Associative Arrays
Chapter 15: Eigenvalues and Eigenvectors
Chapter 16: Higher Dimensions