Mathematics of big data: spreadsheets, databases, matrices, and graphs
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, MA
MIT Press
[2018]
|
| Schriftenreihe: | MIT Lincoln laboratory series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXI, 418 Seiten Illustrationen, Diagramme |
| ISBN: | 9780262038393 |
Internformat
MARC
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Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
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| adam_text | Contents Foreword Preface xiii About the Authors xvii About the Cover xix Acknowledgments I 1 APPLICATIONS AND PRACTICE Introduction and Overview 1.1 1.2 1.3 1.4 1.5 2 3 xi Mathematics of Data Data in the World Mathematical Foundations Making Data Rigorous Conclusions, Exercises, and References xxiii 1 3 3 5 9 14 16 Perspectives on Data 19 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 19 20 22 26 27 29 30 31 Interrelations Spreadsheets Databases Matrices Graphs Map Reduce Other Perspectives Conclusions, Exercises, and References Dynamic Distributed Dimensional Data Model 37 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 37 38 39 40 41 44 49 51 53 Background Design Matrix Mathematics Common SQL, NoSQL, NewSQL Interface Key-Value Store Database Schema Data-lndependent Analytics Parallel Performance Computing on Masked Data Conclusions, Exercises, and References
Associative Arrays and Musical Metadata 57 Data and Metadata Dense Data Dense Operations Sparse Data Sparse Operations Conclusions, Exercises, and References 57 58 60 62 63 65 4.1 4.2 4.3 4.4 4.5 4.6 Associative Arrays and Abstract Art 5.1 5.2 5.3 5.4 5.5 5.6 Visual Abstraction Minimal Adjacency Array Symmetric Adjacency Array Weighted Adjacency Array Incidence Array Conclusions, Exercises, and References Manipulating Graphs with Matrices 6,1 6.2 6.3 6.4 6.5 6.6 Introduction Matrix Indices and Values Composable Graph Operations and Linear Systems Matrix Graph Operations Overview Graph Algorithms and Diverse Semirings Conclusions, Exercises, and References 69 69 71 73 75 75 78 81 81 86 89 96 105 108 Graph Analysis and Machine Learning Systems 115 Introduction Data Representation Graph Construction Adjacency Array Graph Traversal Incidence Array Graph Traversal Vertex Degree Centrality Edge Degree Centrality Eigenvector Centrality Singular Value Decomposition PageRank Deep Neural Networks Conclusions, Exercises, and References 115 116 118 120 122 126 129 129 133 136 138 140 7.1 7,2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 MATHEMATICAL FOUNDATIONS 145 Visualizing the Algebra of Associative Arrays 147 8.1 8.2 8.3 8.4 Associative Array Analogs of Matrix Operations Abstract Algebra for Computer Scientists and Engineers Depicting Mathematics Associative Array Class Diagrams 147 150 152 153
8.5 Set 154 8.6 Semiring 155 8.7 Linear Algebra 158 8.8 Ordered Sets 160 8.9 Boolean Algebra 162 8.10 Associative Array Algebra 8.11 Conclusions, Exercises, and References 164 164 Defining the Algebra of Associative Arrays 169 9.1 Operations on Sets 169 9.2 Ordered Sets 175 9.3 Supremum and Infimum 177 9.4 Lattice 181 9.5 The Semirings of Interest 186 9.6 Conclusions, Exercises, and References 189 Structural Properties of Associative Arrays 10.1 Estimating Structure 193 193 10.2 Associative Array Formal Definition 194 10.3 Padding Associative Arrays with Zeros 197 10.4 Zero, Null, Zero-Sum-Free 198 10.5 Properties of Matrices and Associative Arrays 199 10.6 Properties of Zero Padding 201 10.7 Support and Size 207 10.8 Image and Rank 208 10.9 Example: Music 209 10.10 Example: Art 211 10.11 Properties of Element-Wise Addition 213 10.12 Properties of Element-Wise Multiplication 217 10.13 Array Multiplication 221 10.14 Closure of Operations between Arrays 228 10.15 Conclusions, Exercises, and References 229 Graph Construction and Graphical Patterns 11.1 Introduction 235 235 11.2 Adjacency and Incidence Array Definitions 236 11.3 Adjacency Array Construction 242 11.4 Graph Construction with Different Semirings 250 11.5 Special Arrays and Graphs 255 11.6 Key Ordering 258 11.7 Algebraic Properties 263 11.8 Subobject Properties 264 11.9 Conclusions, Exercises, and References 266
Ill LINEAR SYSTEMS 269 12 Survey of Common Transformations 271 12.1 12.2 12.3 12.4 12.5 12.6 13 14 16 271 274 290 293 297 299 Maps and Bases 303 13.1 13.2 13.3 13.4 13.5 13.6 13.7 303 307 309 312 313 317 320 Semimodules Linear Maps Linear Independence and Bases Existence of Bases Size of Bases Semialgebras and the Algebra of Arrays Conclusions, Exercises, and References Linearity of Associative Arrays 14.1 14.2 14.3 14.4 14.5 14.6 15 Array Transformations Identity Contraction Stretching Rotation Conclusions, Exercises, and References The Null Space of Linear Maps Supremum-Blank Algebras Max-Blank Structure Theorem Examples of Supremum-Blank Algebras Explicit Computations of x(A, w) for Supremum-Blank Algebras Conclusions, Exercises, and References 323 323 326 334 338 342 348 Eigenvalues and Eigenvectors 351 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 351 353 359 360 367 373 378 385 Introduction Quasi-Inverses Existence of Eigenvalues for Idempotent Multiplication Strong Dependence and Characteristic Bipolynomial Eigenanalysis for Irreducible Matrices for Invertible Multiplication Eigen-Semimodules Singular Value Decomposition Conclusions, Exercises, and References Higher Dimensions 389 16.1 ¿-Dimensional Associative Arrays 16.2 Key Ordering and Two-Dimensional Projections 16.3 Algebraic Properties 16.4 Sub-Array Properties 16.5 Conclusions, Exercises, and References 389 392 398 400 402 Appendix: Notation 405 Index 413
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| isbn | 9780262038393 |
| language | English |
| lccn | 2017057054 |
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| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | MIT Press |
| record_format | marc |
| series2 | MIT Lincoln laboratory series |
| spellingShingle | Kepner, Jeremy V. 1969- Mathematics of big data spreadsheets, databases, matrices, and graphs Big data Graphic methods Big Data (DE-588)4802620-7 gnd |
| subject_GND | (DE-588)4802620-7 |
| title | Mathematics of big data spreadsheets, databases, matrices, and graphs |
| title_auth | Mathematics of big data spreadsheets, databases, matrices, and graphs |
| title_exact_search | Mathematics of big data spreadsheets, databases, matrices, and graphs |
| title_full | Mathematics of big data spreadsheets, databases, matrices, and graphs Jeremy Kepner and Hayden Jananthan |
| title_fullStr | Mathematics of big data spreadsheets, databases, matrices, and graphs Jeremy Kepner and Hayden Jananthan |
| title_full_unstemmed | Mathematics of big data spreadsheets, databases, matrices, and graphs Jeremy Kepner and Hayden Jananthan |
| title_short | Mathematics of big data |
| title_sort | mathematics of big data spreadsheets databases matrices and graphs |
| title_sub | spreadsheets, databases, matrices, and graphs |
| topic | Big data Graphic methods Big Data (DE-588)4802620-7 gnd |
| topic_facet | Big data Graphic methods Big Data |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030488842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Inhaltsverzeichnis
Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 ST 530 K38 |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |