Foundations of data science:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York, NY ; New Delhi ; Singapore
Cambridge University Press
2020
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enthält Literaturnachweise und Index. - Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | viii, 424 Seiten Diagramme |
| ISBN: | 9781108485067 |
Staff View
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Contents 1 Introduction page 1 2 High-Dimensional Space 2.1 Introduction 2.2 The Law of Large Numbers 2.3 The Geometry of High Dimensions 2.4 Properties of the Unit Ball 2.5 Generating Points Uniformly at Random from a Ball 2.6 Gaussiane in High Dimension 2.7 Random Projection and Johnson-Lindenstrauss Lemma 2.8 Separating Gaussiane 2.9 Fitting a Spherical Gaussian to Data 2.10 Bibliographic Notes 2.11 Exercises 4 4 4 8 8 13 15 16 18 20 21 22 3 Best-Fit Subspaces and Singular Value Decomposition (SVD) 3.1 Introduction 3.2 Preliminaries 3.3 Singular Vectors 3.4 Singular Value Decomposition (SVD) 3.5 Best Rank-/: Approximations 3.6 Left Singular Vectors 3.7 Power Method for Singular Value Decomposition 3.8 Singular Vectors and Eigenvectors 3.9 Applications of Singular Value Decomposition 3.10 Bibliographic Notes 3.11 Exercises 29 29 31 31 34 36 37 39 42 42 53 54 4 Random Walks and Markov Chains 4.1 Stationary Distribution 4.2 Markov Chain Monte Carlo 4.3 Areas and Volumes 4.4 Convergence of Random Walks on Undirected Graphs 4.5 Electrical Networks and Random Walks 4.6 Random Walks on Undirected Graphs with Unit Edge Weights 62 65 67 71 73 81 85 --------- v ---------
CONTENTS Random Walks in Euclidean Space 4.7 The Web as a Markov Chain 4.8 Bibliographic Notes 4.9 4.10 Exercises Machine Learning 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 Introduction The Perceptron Algorithm Kernel Functions and Nonlinearly Separable Data Generalizing to New Data VC-Dimension VC-Dimension and Machine Learning Other Measures of Complexity Deep Learning Gradient Descent Online Learning Boosting Further Current Directions Bibliographic Notes Exercises 6 Algorithms for Massive Data Problems: Streaming, Sketching, and Sampling 6.1 6.2 6.3 6.4 6.5 6.6 Introduction Frequency Moments of Data Streams Matrix Algorithms Using Sampling Sketches of Documents Bibliographic Notes Exercises Introduction /c-Means Clustering UCenter Clustering Finding Low-Error Clusterings Spectral Clustering Approximation Stability High-Density Clusters Kernel Methods Recursive Clustering Based on Sparse Cuts Dense Submatrices and Communities Community Finding and Graph Partitioning Spectral Clustering Applied to Social Networks Bibliographic Notes Exercises 159 159 160 169 177 178 179 182 185 189 189 190 197 199 201 202 202 205 208 210 210 215 215 Random Graphs 8.1 109 109 110 111 113 118 126 127 128 134 138 145 148 152 152 182 Clustering 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 92 95 98 99 The G{n,p) Model vi
CONTENTS 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 Phase Transitions Giant Component Cycles and Full Connectivity Phase Transitions for Increasing Properties Branching Processes CNF-SAT Nonuniform Models of Random Graphs Growth Models Small-World Graphs Bibliographic Notes Exercises 222 232 235 239 241 246 252 254 261 266 266 9 Topic Models, Nonnegative Matrix Factorization, Hidden Markov Models, and Graphical Models 9.1 Topic Models 9.2 An Idealized Model 9.3 Nonnegative Matrix Factorization 9.4 NMF with Anchor Terms 9.5 Hard and Soft Clustering 9.6 The Latent Dirichlet Allocation Model for Topic Modeling 9.7 The Dominant Admixture Model 9.8 Formal Assumptions 9.9 Finding the Term-Topic Matrix 9.10 Hidden Markov Models 9.11 Graphical Models and Belief Propagation 9.12 Bayesian or Belief Networks 9.13 Markov Random Fields 9.14 Factor Graphs 9.15 Tree Algorithms 9.16 Message Passing in General Graphs 9.17 Warning Propagation 9.18 Correlation between Variables 9.19 Bibliographic Notes 9.20 Exercises 274 274 277 279 281 282 283 285 287 290 295 298 299 300 301 301 303 310 311 315 315 10 Other Topics 10.1 Ranking and Social Choice 10.2 Compressed Sensing and Sparse Vectors 10.3 Applications 10.4 An Uncertainty Principle 10.5 Gradient 10.6 Linear Programming 10.7 Integer Optimization 10.8 Semi-Definite Programming 10.9 Bibliographic Notes 10.10 Exercises 318 318 322 325 327 330 332 334 334 336 337
CONTENTS 11 Wavelets 11.1 Dilation 11.2 The Haar Wavelet 11.3 Wavelet Systems 11.4 Solving the Dilation Equation 11.5 Conditions on the Dilation Equation 11.6 Derivation of the Wavelets from the Scaling Function 11.7 Sufficient Conditions for the Wavelets to Be Orthogonal 11.8 Expressing a Function in Terms of Wavelets 11.9 Designing a Wavelet System 11.10 Applications 11.11 Bibliographic Notes 11.12 Exercises 341 341 342 345 346 347 350 353 355 356 357 357 357 12 Background Material 12.1 Definitions and Notation 12.2 Useful Relations 12.3 Useful Inequalities 12.4 Probability 12.5 Bounds on Tail Probability 12.6 Applications of the Tail Bound 12.7 Eigenvalues and Eigenvectors 12.8 Generating Functions 12.9 Miscellaneous 12.10 Exercises 360 360 361 365 372 380 386 387 400 404 407 References Index 411 421 viii |
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| spellingShingle | Blum, Avrim 1966- Hopcroft, John E. 1939- Kannan, Ravindran 1953- Foundations of data science Komplexes System (DE-588)4114261-5 gnd Big Data (DE-588)4802620-7 gnd Datenanalyse (DE-588)4123037-1 gnd Informatik (DE-588)4026894-9 gnd Data Science (DE-588)1140936166 gnd |
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| title | Foundations of data science |
| title_auth | Foundations of data science |
| title_exact_search | Foundations of data science |
| title_full | Foundations of data science Avrim Blum (Toyota Technical Institute at Chicago), John Hopcroft (Cornell University, New York), Ravindran Kannan (Microsoft Research, India) |
| title_fullStr | Foundations of data science Avrim Blum (Toyota Technical Institute at Chicago), John Hopcroft (Cornell University, New York), Ravindran Kannan (Microsoft Research, India) |
| title_full_unstemmed | Foundations of data science Avrim Blum (Toyota Technical Institute at Chicago), John Hopcroft (Cornell University, New York), Ravindran Kannan (Microsoft Research, India) |
| title_short | Foundations of data science |
| title_sort | foundations of data science |
| topic | Komplexes System (DE-588)4114261-5 gnd Big Data (DE-588)4802620-7 gnd Datenanalyse (DE-588)4123037-1 gnd Informatik (DE-588)4026894-9 gnd Data Science (DE-588)1140936166 gnd |
| topic_facet | Komplexes System Big Data Datenanalyse Informatik Data Science Einführung |
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Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 ST 530 B658 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |