Verfügbarkeit: Mathematical foundations of data science using R

Mathematical foundations of data science using R:

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Bibliographische Detailangaben
Beteiligte Personen:	Emmert-Streib, Frank (VerfasserIn), Moutari, Salissou (VerfasserIn), Dehmer, Matthias 1968- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Boston De Gruyter [2020]
Schriftenreihe:	De Gruyter Oldenbourg STEM
Schlagwörter:	Data Mining R > Programm Data Science Mathematik Lehrbuch
Links:	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110564679&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031582132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 414 Seiten Illustrationen, Diagramme 24 cm x 17 cm
ISBN:	9783110564679 311056467X

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS PREFACE ---- V 1 INTRODUCTION ---- 1 1.1 RELATIONSHIPS BETWEEN MATHEMATICAL SUBJECTS AND DATA SCIENCE ----- 2 1.2 STRUCTURE OF THE BOOK ----- 4 1.2.1 PARTONE ----- 4 1.2.2 PART TWO ----- 4 1.2.3 PART THREE ----- 5 1.3 OUR MOTIVATION FOR WRITING THIS BOOK ----- 5 1.4 EXAMPLES AND LISTINGS ----- 6 1.5 HOW TO USE THIS BOOK ----- 7 PART I: INTRODUCTION TO R 2 OVERVIEW OF PROGRAMMING PARADIGMS ---- 11 2.1 INTRODUCTION ----- 11 2.2 IMPERATIVE PROGRAMMING ----- 12 2.3 FUNCTIONAL PROGRAMMING ----- 13 2.4 OBJECT-ORIENTED PROGRAMMING ----- 15 2.5 LOGIC PROGRAMMING ----- 17 2.6 OTHER PROGRAMMING PARADIGMS ----- 18 2.6.1 THE MULTIPARADIGM LANGUAGE R ------ 18 2.7 COMPILER VERSUS INTERPRETER LANGUAGES ----- 20 2.8 SEMANTICS OF PROGRAMMING LANGUAGES ----- 21 2.9 FURTHER READING ----- 22 2.10 SUMMARY ----- 22 3 SETTING UP AND INSTALLING THE R PROGRAM ---- 23 3.1 INSTALLING R ON LINUX ----- 23 3.2 INSTALLING R ON MAC OS X ----- 24 3.3 INSTALLING R ON WINDOWS ----- 24 3.4 USING R ------ 24 3.5 SUMMARY ----- 24 4 INSTALLATION OF R PACKAGES ---- 27 4.1 INSTALLING PACKAGES FROM CRAN ----- 27 4.2 INSTALLING PACKAGES FROM BIOCONDUCTOR ------ 27 4.3 INSTALLING PACKAGES FROM GITHUB ----- 28 4.4 INSTALLING PACKAGES MANUALLY ------ 28 VIII * CONTENTS 4.4.1 4.4.2 4.5 4.6 TERMINAL AND UNIX COMMANDS ----- 28 PACKAGE INSTALLATION ----- 29 ACTIVATION OF A PACKAGE IN AN R SESSION ----- 30 SUMMARY ----- 30 5 5.1 5.1.1 5.1.2 5.1.3 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 5.2.6 5.2.7 5.2.8 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.3.7 5.3.8 5.3.9 5.3.10 5.4 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.5 5.6 5.6.1 5.6.2 5.6.3 5.6.4 INTRODUCTION TO PROGRAMMING IN R ---- 31 BASIC ELEMENTS OF R ----- 31 NAVIGATING DIRECTORIES ----- 32 SYSTEM FUNCTIONS ----- 32 GETTING HELP ----- 33 BASIC PROGRAMMING ----- 34 IF-CLAUSE ----- 34 SWITCH ----- 35 LOOPS ----- 36 FOR-LOOP ----- 36 WHILE-LOOP ----- 36 LOGIC BEHIND A FOR-LOOP ----- 37 BREAK ----- 40 REPEAT-LOOP ----- 40 DATA STRUCTURES ----- 41 VECTOR ----- 41 MATRIX ----- 43 LIST ----- 46 ARRAY ----- 47 DATA FRAME ----- 48 ENVIRONMENT ----- 49 REMOVING VARIABLES FROM THE WORKSPACE ----- 50 FACTOR ----- 50 DATE AND TIME ----- 51 INFORMATION ABOUT R OBJECTS ----- 52 HANDLING CHARACTER STRINGS ----- 52 THE FUNCTION NCHAR() ----- 52 THE FUNCTION PASTE() ----- 53 THE FUNCTION SUBSTR() ----- 53 THE FUNCTION STRSPLIT() ----- 54 REGULAR EXPRESSIONS ----- 55 SORTING VECTORS ----- 57 WRITING FUNCTIONS ----- 58 ONE INPUT ARGUMENT AND ONE OUTPUT VALUE ----- 58 SCOPE OF VARIABLES ----- 61 ONE INPUT ARGUMENT, MANY OUTPUT VALUES ----- 61 MANY INPUT ARGUMENTS, MANY OUTPUT VALUES ----- 62 CONTENTS * IX 5.7 5.7.1 5.7.2 5.7.3 5.7.4 5.7.5 5.8 5.8.1 5.8.2 5.8.3 5.8.4 5.8.5 5.8.6 5.8.7 5.8.8 5.9 5.9.1 5.10 WRITING AND READING DATA ----- 62 WRITING DATA TO A FILE ----- 63 READING DATA FROM A FILE ----- 64 LOW LEVEL READING FUNCTIONS ----- 66 SUMMARY OF WRITING AND READING FUNCTIONS ----- 68 OTHER DATA FORMATS ----- 68 USEFUL COMMANDS ----- 69 THE FUNCTION WHICH() ----- 69 THE FUNCTION APPLY() ----- 70 SET COMMANDS ----- 71 THE FUNCTION UNIQUE() ----- 72 TESTING ARGUMENTS AND CONVERTING VARIABLES ----- 72 THE FUNCTION SAMPLE() ----- 73 THE FUNCTION TRY() ----- 74 THE FUNCTION SYSTEM() ----- 75 PRACTICAL USAGE OF R ----- 76 ADVANTAGE OVER GUI SOFTWARE ----- 76 SUMMARY ----- 77 6 6.1 6.1.1 6.1.2 6.1.3 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.3 6.3.1 6.3.2 6.3.3 6.4 6.4.1 6.4.2 6.5 6.6 6.7 6.7.1 6.8 CREATING R PACKAGES ---- 79 REQUIREMENTS ----- 79 R BASE PACKAGES ----- 79 R REPOSITORIES ----- 80 RTOOLS ----- 80 R CODE OPTIMIZATION ----- 81 PROFILING AN R SCRIPT ----- 81 BYTE CODE COMPILATION ----- 81 GPU LIBRARY, CODE, AND OTHERS ----- 82 EXCEPTION HANDLING ----- 82 S3, S4, AND RC OBJECT-ORIENTED SYSTEMS ----- 83 THE S3 CLASS ----- 84 THE S4 CLASS ----- 85 REFERENCE CLASS (RC) SYSTEM ----- 86 CREATING AN R PACKAGE BASED ON THE S3 CLASS SYSTEM ----- 87 R PROGRAM FILE ----- 87 BUILDING AN R PACKAGE ----- 90 CHECKING THE PACKAGE ----- 90 INSTALLATION AND USAGE OF THE PACKAGE ----- 90 LOADING AND USING A PACKAGE ----- 91 CONTENT OF THE FILES EDITED WHEN GENERATING THE PACKAGE ----- 91 SUMMARY ----- 94 X * CONTENTS PART II: GRAPHICS IN R 7 7.1 7.1.1 7.1.2 7.1.3 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 BASIC PLOTTING FUNCTIONS ---- 97 PLOT ----- 97 ADDING MULTIPLE CURVES IN ONE PLOT ----- 99 ADDING HORIZONTAL AND VERTICAL LINES ----- 101 OPENING A NEW FIGURE WINDOW ----- 102 HISTOGRAMS ----- 102 BAR PLOTS ----- 103 PIE CHARTS ----- 104 DOT PLOTS ----- 105 STRIP AND RUG PLOTS ----- 108 DENSITY PLOTS ----- 109 COMBINING A SCATTERPLOT WITH HISTOGRAMS: THE LAYOUT FUNCTION ----- 112 THREE-DIMENSIONAL PLOTS ----- 114 CONTOUR AND IMAGE PLOTS ----- 114 SUMMARY ----- 115 8 8.1 8.2 8.3 8.3.1 8.3.2 8.3.3 8.3.4 8.4 ADVANCED PLOTTING FUNCTIONS: GGPLOT2 ---- 117 INTRODUCTION ----- 117 QPLOT() ----- 117 GGPLOT() ----- 121 SIMPLE EXAMPLES ----- 121 MULTIPLE DATA SETS ----- 123 GEOMS() ----- 125 SMOOTHING ----- 128 SUMMARY ----- 131 9 9.1 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.3.5 VISUALIZATION OF NETWORKS ---- 133 INTRODUCTION ----- 133 IGRAPH ----- 133 GENERATION OF REGULAR AND COMPLEX NETWORKS ----- 135 BASIC NETWORK ATTRIBUTES ----- 136 LAYOUT STYLES ----- 139 PLOTTING NETWORKS ----- 140 ANALYZING AND MANIPULATING NETWORKS ----- 141 NETBIOV ----- 141 GLOBAL NETWORK LAYOUT ----- 142 MODULAR NETWORK LAYOUT ----- 142 LAYERED NETWORK (MULTIROOT) LAYOUT ----- 144 FURTHER FEATURES ----- 144 EXAMPLES: VISUALIZATION OF NETWORKS USING NETBIOV ----- 146 CONTENTS * XI 9.4 SUMMARY ----- 149 PART III: MATHEMATICAL BASICS OF DATA SCIENCE 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 MATHEMATICS AS A LANGUAGE FOR SCIENCE ---- 153 INTRODUCTION ----- 153 NUMBERS AND NUMBER OPERATIONS ----- 155 SETS AND SET OPERATIONS ----- 157 BOOLEAN LOGIC ----- 159 SUM, PRODUCT, AND BINOMIAL COEFFICIENTS ----- 162 FURTHER SYMBOLS ----- 164 IMPORTANCE OF DEFINITIONS AND THEOREMS ----- 167 SUMMARY ----- 168 11 11.1 11.2 11.3 11.4 11.5 11.5.1 11.5.2 11.5.3 11.5.4 11.6 COMPUTABILITY AND COMPLEXITY ---- 171 INTRODUCTION ----- 171 A BRIEF HISTORY OF COMPUTER SCIENCE ----- 172 TURING MACHINES ----- 173 COMPUTABILITY ----- 174 COMPLEXITY OF ALGORITHMS ----- 175 BOUNDS ----- 176 EXAMPLES ----- 178 IMPORTANT PROPERTIES OF THE O-NOTATION ----- 179 KNOWN COMPLEXITY CLASSES ----- 179 SUMMARY ----- 180 12 12.1 12.1.1 12.1.2 12.1.3 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.8.1 12.8.2 12.8.3 LINEAR ALGEBRA ---- 181 VECTORS AND MATRICES ----- 181 VECTORS ----- 181 VECTOR REPRESENTATIONS IN OTHER COORDINATES SYSTEMS ----- 193 MATRICES ----- 202 OPERATIONS WITH MATRICES ----- 205 SPECIAL MATRICES ----- 208 TRACE AND DETERMINANT OF A MATRIX ----- 210 SUBSPACES, DIMENSION, AND RANK OF A MATRIX ----- 211 EIGENVALUES AND EIGENVECTORS OF A MATRIX ----- 214 MATRIX NORMS ----- 216 MATRIX FACTORIZATION ----- 217 LU FACTORIZATION ----- 217 CHOLESKY FACTORIZATION ----- 220 QR FACTORIZATION ----- 220 XII * CONTENTS 12.8.4 12.9 12.10 SINGULAR VALUE DECOMPOSITION ----- 222 SYSTEMS OF LINEAR EQUATIONS ----- 224 EXERCISES ----- 227 13 13.1 13.2 13.3 13.4 13.5 13.6 13.6.1 13.6.2 13.7 13.8 13.9 13.10 ANALYSIS ---- 229 INTRODUCTION ----- 229 LIMITING VALUES ----- 229 DIFFERENTIATION ----- 232 EXTREMA OF A FUNCTION ----- 236 TAYLOR SERIES EXPANSION ----- 239 INTEGRALS ----- 243 PROPERTIES OF DEFINITE INTEGRALS ----- 244 NUMERICAL INTEGRATION ----- 244 POLYNOMIAL INTERPOLATION ----- 245 ROOT FINDING METHODS ----- 247 FURTHER READING ----- 251 EXERCISES ----- 251 14 14.1 14.1.1 14.2 14.2.1 14.2.2 14.2.3 14.2.4 14.3 DIFFERENTIAL EQUATIONS ---- 253 ORDINARY DIFFERENTIAL EQUATIONS (ODE) ----- 253 INITIAL VALUE ODE PROBLEMS ----- 253 PARTIAL DIFFERENTIAL EQUATIONS (PDE) ----- 258 FIRST-ORDER PDE ----- 259 SECOND-ORDER PDE ----- 259 BOUNDARY AND INITIAL CONDITIONS ----- 260 WELL-POSED PDE PROBLEMS ----- 260 EXERCISES ----- 265 15 15.1 15.2 15.2.1 15.2.2 15.2.3 15.3 15.4 15.5 15.6 15.6.1 15.6.2 15.6.3 15.6.4 DYNAMICAL SYSTEMS ---- 267 INTRODUCTION ----- 267 POPULATION GROWTH MODELS ----- 269 EXPONENTIAL POPULATION GROWTH MODEL ----- 269 LOGISTIC POPULATION GROWTH MODEL ----- 269 LOGISTIC MAP ----- 271 THE LOTKA-VOLTERRA OR PREDATOR-PREY SYSTEM ----- 275 CELLULAR AUTOMATA ----- 278 RANDOM BOOLEAN NETWORKS ----- 281 CASE STUDIES OF DYNAMICAL SYSTEM MODELS WITH COMPLEX ATTRACTORS ----- 288 THE LORENZ ATTRACTOR ----- 288 CLIFFORD ATTRACTOR ----- 290 IKEDA ATTRACTOR ----- 291 THE PETER DE JONG ATTRACTOR ----- 292 CONTENTS XIII 15.6.5 ROSSLER ATTRACTOR ------- 293 15.7 FRACTALS ----- 294 15.7.1 THE SIERPIHSKY CARPET AND TRIANGLE ----- 294 15.7.2 THE BARNSLEY FERN 296 15.7.3 JULIA SETS ------ 298 15.7.4 MANDELBROT SET ------ 300 15.8 EXERCISES ------ 302 16 GRAPH THEORY AND NETWORK ANALYSIS ---- 305 16.1 INTRODUCTION ------ 305 16.2 BASIC TYPES OF NETWORKS ----- 306 16.2.1 UNDIRECTED NETWORKS ----- 306 16.2.2 GEOMETRIC VISUALIZATION OF NETWORKS ----- 307 16.2.3 DIRECTED AND WEIGHTED NETWORKS ----- 308 16.2.4 WALKS, PATHS, AND DISTANCES IN NETWORKS ----- 310 16.3 QUANTITATIVE NETWORK MEASURES ----- 311 16.3.1 DEGREE AND DEGREE DISTRIBUTION ----- 311 16.3.2 CLUSTERING COEFFICIENT ----- 312 16.3.3 PATH-BASED MEASURES ----- 312 16.3.4 CENTRALITY MEASURES ----- 313 16.4 GRAPH ALGORITHMS ----- 314 16.4.1 BREADTH-FIRST SEARCH ----- 315 16.4.2 DEPTH-FIRST SEARCH ----- 315 16.4.3 SHORTEST PATHS ----- 317 16.4.4 MINIMUM SPANNING TREE ----- 321 16.5 NETWORK MODELS AND GRAPH CLASSES ------ 323 16.5.1 TREES ----- 323 16.5.2 GENERALIZED TREES ----- 324 16.5.3 RANDOM NETWORKS ----- 325 16.5.4 SMALL-WORLD NETWORKS ----- 326 16.5.5 SCALE-FREE NETWORKS ----- 328 16.6 FURTHER READING ----- 329 16.7 SUMMARY ----- 330 16.8 EXERCISES ----- 330 17 PROBABILITY THEORY ---- 331 17.1 EVENTS AND SAMPLE SPACE ----- 331 17.2 SET THEORY ----- 332 17.3 DEFINITION OF PROBABILITY ----- 334 17.4 CONDITIONAL PROBABILITY ----- 335 17.5 CONDITIONAL PROBABILITY AND INDEPENDENCE ----- 336 17.6 RANDOM VARIABLES AND THEIR DISTRIBUTION FUNCTION ----- 337 XIV * CONTENTS 17.7 DISCRETE AND CONTINUOUS DISTRIBUTIONS ----- 338 17.7.1 UNIFORM DISTRIBUTION ---- 339 17.8 EXPECTATION VALUES AND MOMENTS ------ 340 17.8.1 EXPECTATION VALUES ------ 340 17.8.2 VARIANCE ------ 341 17.8.3 MOMENTS ------ 341 17.8.4 COVARIANCE AND CORRELATION ----- 342 17.9 BIVARIATE DISTRIBUTIONS ----- 343 17.10 MULTIVARIATE DISTRIBUTIONS ----- 343 17.11 IMPORTANT DISCRETE DISTRIBUTIONS ----- 344 17.11.1 BERNOULLI DISTRIBUTION ------ 345 17.11.2 BINOMIAL DISTRIBUTION ------ 345 17.11.3 GEOMETRIC DISTRIBUTION ----- 348 17.11.4 NEGATIVE BINOMIAL DISTRIBUTION ----- 348 17.11.5 POISSON DISTRIBUTION ------ 349 17.12 IMPORTANT CONTINUOUS DISTRIBUTIONS ----- 350 17.12.1 EXPONENTIAL DISTRIBUTION ----- 350 17.12.2 BETA DISTRIBUTION ----- 350 17.12.3 GAMMA DISTRIBUTION ------ 351 17.12.4 NORMAL DISTRIBUTION ------ 353 17.12.5 CHI-SQUARE DISTRIBUTION ----- 355 17.12.6 STUDENT * S ^-DISTRIBUTION ----- 355 17.12.7 LOG-NORMAL DISTRIBUTION ----- 357 17.12.8 WEIBULL DISTRIBUTION ------ 357 17.13 BAYES * THEOREM ----- 358 17.14 INFORMATION THEORY ----- 361 17.14.1 ENTROPY ----- 362 17.14.2 KULLBACK-LEIBLER DIVERGENCE - 364 17.14.3 MUTUAL INFORMATION ------ 365 17.15 LAW OF LARGE NUMBERS ------ 366 17.16 CENTRAL LIMIT THEOREM ----- 369 17.17 CONCENTRATION INEQUALITIES ---- 369 17.17.1 HOEFFDING* S INEQUALITY ------ 370 17.17.2 CAUCHY-SCHWARTZ INEQUALITY - 370 17.17.3 CHERNOFF BOUNDS ----- 371 17.18 FURTHER READING ----- 372 17.19 SUMMARY ----- 372 17.20 EXERCISES ----- 372 18 OPTIMIZATION ----- 375 18.1 INTRODUCTION ----- 375 18.2 FORMULATION OF AN OPTIMIZATION PROBLEM ----- 376 CONTENTS * XV 18.3 18.3.1 18.3.2 18.4 18.4.1 18.4.2 18.4.3 18.5 18.5.1 18.5.2 18.6 18.7 18.8 UNCONSTRAINED OPTIMIZATION PROBLEMS ----- 377 GRADIENT-BASED METHODS ----- 377 DERIVATIVE-FREE METHODS ----- 385 CONSTRAINED OPTIMIZATION PROBLEMS ----- 390 CONSTRAINED LINEAR OPTIMIZATION PROBLEMS ----- 390 CONSTRAINED NONLINEAR OPTIMIZATION PROBLEMS ----- 394 LAGRANGE MULTIPLIER METHOD ----- 394 SOME APPLICATIONS IN STATISTICAL MACHINE LEARNING ----- 396 MAXIMUM LIKELIHOOD ESTIMATION ----- 397 SUPPORT VECTOR CLASSIFICATION ----- 398 FURTHER READING ----- 399 SUMMARY ----- 399 EXERCISES ----- 400 BIBLIOGRAPHY ---- 403 INDEX ---- 411
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genre_facet	Lehrbuch
id	DE-604.BV046203036
illustrated	Illustrated
indexdate	2025-01-29T17:02:52Z
institution	BVB
institution_GND	(DE-588)10095502-2
isbn	9783110564679 311056467X
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-031582132
oclc_num	1164650397
open_access_boolean
owner	DE-20 DE-706 DE-1050 DE-703 DE-1043 DE-83 DE-91G DE-BY-TUM DE-11 DE-945
owner_facet	DE-20 DE-706 DE-1050 DE-703 DE-1043 DE-83 DE-91G DE-BY-TUM DE-11 DE-945
physical	XV, 414 Seiten Illustrationen, Diagramme 24 cm x 17 cm
publishDate	2020
publishDateSearch	2020
publishDateSort	2020
publisher	De Gruyter
record_format	marc
series2	De Gruyter Oldenbourg STEM
spellingShingle	Emmert-Streib, Frank Moutari, Salissou Dehmer, Matthias 1968- Mathematical foundations of data science using R Data Mining (DE-588)4428654-5 gnd R Programm (DE-588)4705956-4 gnd Data Science (DE-588)1140936166 gnd Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4428654-5 (DE-588)4705956-4 (DE-588)1140936166 (DE-588)4037944-9 (DE-588)4123623-3
title	Mathematical foundations of data science using R
title_auth	Mathematical foundations of data science using R
title_exact_search	Mathematical foundations of data science using R
title_full	Mathematical foundations of data science using R Frank Emmert-Streib, Salissou Moutari, and Matthias Dehmer
title_fullStr	Mathematical foundations of data science using R Frank Emmert-Streib, Salissou Moutari, and Matthias Dehmer
title_full_unstemmed	Mathematical foundations of data science using R Frank Emmert-Streib, Salissou Moutari, and Matthias Dehmer
title_short	Mathematical foundations of data science using R
title_sort	mathematical foundations of data science using r
topic	Data Mining (DE-588)4428654-5 gnd R Programm (DE-588)4705956-4 gnd Data Science (DE-588)1140936166 gnd Mathematik (DE-588)4037944-9 gnd
topic_facet	Data Mining R Programm Data Science Mathematik Lehrbuch
url	http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110564679&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031582132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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