A probabilistic theory of pattern recognition:
Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed. The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches. The book includes a discussion of distance me...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1996
|
| Series: | Applications of mathematics
31 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed. The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches. The book includes a discussion of distance measures, nonparametric methods based on kernels or nearest neighbors, Vapnik-Chervonenkis theory, epsilon entropy, parametric classification, error estimation, tree classifiers, and neural networks Wherever possible, distribution-free properties and inequalities are derived. A substantial portion of the results or the analysis is new. Over 430 problems and exercises complement the material |
| Physical Description: | XV, 636 S. Diagramme |
| ISBN: | 0387946187 9780387946184 |
Staff View
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| 490 | 1 | |a Applications of mathematics |v 31 | |
| 520 | 3 | |a Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed. The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches. The book includes a discussion of distance measures, nonparametric methods based on kernels or nearest neighbors, Vapnik-Chervonenkis theory, epsilon entropy, parametric classification, error estimation, tree classifiers, and neural networks | |
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Contents Preface v 1 1 Introduction 2 The Bayes Error 2.1 The Bayes Problem 2.2 A Simple Example 2.3 Another Simple Example 2.4 Other Formulas for the Bayes Risk 2.5 Plug-In Decisions 2.6 Bayes Error Versus Dimension Problems and Exercises 9 9 11 12 14 15 17 18 3 Inequalities and Alternate Distance Measures 3.1 Measuring Discriminatory Information 3.2 The Kolmogorov Variational Distance 3.3 The Nearest Neighbor Error 3.4 The Bhattacharyya Affinity 3.5 Entropy 3.6 Jeffreys’ Divergence 3.7 F-Errors 3.8 The Mahalanobis Distance 3.9 /-Divergences Problems and Exercises 21 21 22 22 23 25 27 28 30 31 35
X Contents 4 Linear Discrimination 4.1 Univariate Discrimination and Stoller Splits 4.2 Linear Discriminants 4.3 The Fisher Linear Discriminant 4.4 The Normal Distribution 4.5 Empirical Risk Minimization 4.6 Minimizing Other Criteria Problems and Exercises 39 40 44 46 47 49 54 56 5 Nearest Neighbor Rules 5.1 Introduction 5.2 Notation and Simple Asymptotics 5.3 Proof of Stone’s Lemma 5.4 The Asymptotic Probability of Error 5.5 The Asymptotic Error Probability of Weighted Nearest Neighbor Rules 5.6 k-Nearest Neighbor Rules: Even к 5.7 Inequalities for the Probability of Error 5.8 Behavior When L* Is Small 5.9 Nearest Neighbor Rules When L* = 0 5.10 Admissibility of the Nearest Neighbor Rule 5.11 The (k, /)-Nearest Neighbor Rule Problems and Exercises 61 61 63 66 69 71 74 75 78 80 81 81 83 6 Consistency 6.1 Universal Consistency 6.2 Classification and Regression Estimation 6.3 Partitioning Rules 6.4 The Histogram Rule 6.5 Stone’s Theorem 6.6 The k-Nearest Neighbor Rule 6.7 Classification Is Easier Than RegressionFunction Estimation 6.8 Smart Rules Problems and Exercises 91 91 92 94 95 97 100 101 106 107 7 Slow Rates of Convergence 7.1 Finite Training Sequence 7.2 Slow Rates Problems and Exercises 111 111 113 118 8 Error Estimation 8.1 Error Counting 8.2 Hoeffding’s Inequality 8.3 Error Estimation Without Testing Data 8.4 Selecting Classifiers 121 121 122 124 125
Contents 8.5 Estimating the Bayes Error Problems and Exercises xi 128 129 9 The Regular Histogram Rule 9.1 The Method of Bounded Differences 9.2 Strong Universal Consistency Problems and Exercises 133 133 138 142 10 Kernel Rules 10.1 Consistency 10.2 Proof of the Consistency Theorem 10.3 Potential Function Rules Problems and Exercises 147 149 153 159 161 11 Consistency of the ^-Nearest Neighbor Rule 11.1 Strong Consistency 11.2 Breaking Distance Ties 11.3 Recursive Methods 11.4 Scale-Invariant Rules 11.5 Weighted Nearest Neighbor Rules 11.6 Rotation-Invariant Rules 11.7 Relabeling Rules Problems and Exercises 169 170 174 176 177 178 179 180 182 12 Vapnik-Chervonenkis Theory 12.1 Empirical Error Minimization 12.2 Fingering 12.3 The Glivenko-Cantelli Theorem 12.4 Uniform Deviations of Relative Frequencies from Probabilities 12.5 Classifier Selection 12.6 Sample Complexity 12.7 The Zero-Ercor Case 12.8 Extensions Problems and Exercises 187 187 191 192 196 199 201 202 206 208 13 Combinatorial Aspects of Vapnik-Chervonenkis Theory 13.1 Shatter Coefficients and VC Dimension 13.2 Shatter Coefficients of Some Classes 13.3 Linear and Generalized Linear Discrimination Rules 13.4 Convex Sets and Monotone Layers Problems and Exercises 215 215 219 224 226 229 14 Lower Bounds for Empirical Classifier Selection 14.1 Minimax Lower Bounds 14.2 The Case Lc =0 14.3 Classes with Infinite VC Dimension 233 234 234 238
xii Contents 14.4 The Case Le 0 14.5 Sample Complexity Problems and Exercises 239 245 247 15 The Maximum Likelihood Principle 15.1 Maximum Likelihood: The Formats 15.2 The Maximum Likelihood Method: Regression Format 15.3 Consistency 15.4 Examples 15.5 Classical Maximum Likelihood: Distribution Format Problems and Exercises 249 249 250 253 256 260 261 16 Parametric Classification 16.1 Example: Exponential Families 16.2 Standard Plug-In Rules 16.3 Minimum Distance Estimates 16.4 Empirical Error Minimization Problems and Exercises 263 266 267 270 275 276 17 Generalized Linear Discrimination 17.1 Fourier Series Classification 17.2 Generalized Linear Classification Problems and Exercises 279 280 285 287 18 Complexity Regularization 18.1 Structural Risk Minimization 18.2 Poor Approximation Properties of VC Classes 18.3 Simple Empirical Covering Problems and Exercises 289 290 297 297 300 19 Condensed and Edited Nearest Neighbor Rules 19.1 Condensed Nearest Neighbor Rules 19.2 Edited Nearest Neighbor Rules 19.3 Sieves and Prototypes Problems and Exercises 303 303 309 309 312 20 Tree 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 315 318 319 322 326 328 332 333 334 336 Classifiers Invariance Trees with the X-Property Balanced Search Trees Binary Search Trees The Chronological к-d Tree The Deep к-d Tree Quadtrees Best Possible Perpendicular Splits Splitting Criteria Based on Impurity Functions
Contents 20.10 A Consistent SplittingCriterion 20.11 BSP Trees 20.12 Primitive Selection 20.13 Constructing Consistent Tree Classifiers 20.14 A Greedy Classifier Problems and Exercises 21 Data-Dependent Partitioning 21.1 Introduction 21.2 A Vapnik-Chervonenkis Inequality for Partitions 21.3 Consistency 21.4 Statistically Equivalent Blocks 21.5 Partitioning Rules Based on Clustering 21.6 Data-Based Scaling 21.7 Classification Trees Problems and Exercises 22 Splitting the Data 22.1 The Holdout Estimate 22.2 Consistency and Asymptotic Optimality 22.3 Nearest Neighbor Rules with Automatic Scaling 22.4 Classification Based on Clustering 22.5 Statistically Equivalent Blocks 22.6 Binary Tree Classifiers Problems and Exercises 23 The Resubstitution Estimate 23.1 The Resubstitution Estimate 23.2 Histogram Rules 23.3 Data-Based Histograms and Rule Selection Problems and Exercises 24 Deleted Estimates of the Error Probability 24.1 A General Lower Bound 24.2 A General Upper Bound for Deleted Estimates 24.3 Nearest Neighbor Rules 24.4 Kernel Rules 24.5 Histogram Rules Problems and Exercises 25 Automatic Kernel Rules 25.1 25.2 25.3 25.4 Consistency Data Splitting Kernel Complexity Multiparameter Kernel Rules xiii 340 341 343 346 348 357 363 363 364 368 372 377 381 383 383 387 387 389 391 392 393 394 395 397 397 399 403 405 407 408 411 413 415 417 419 423 424 428 431 435
xiv Contents 25.5 Kernels of Infinite Complexity 25.6 On Minimizing the Apparent Error Rate 25.7 Minimizing the Deleted Estimate 25.8 Sieve Methods 25.9 Squared Error Minimization Problems and Exercises 436 439 441 444 445 446 26 Automatic Nearest Neighbor Rules 26.1 Consistency 26.2 Data Splitting 26.3 Data Splitting for Weighted NN Rules 26.4 Reference Data and Data Splitting 26.5 Variable Metric NN Rules 26.6 Selection of к Based on the Deleted Estimate Problems and Exercises 451 451 452 453 454 455 457 458 27 Hypercubes and Discrete Spaces 27.1 Multinomial Discrimination 27.2 Quantization 27.3 Independent Components 27.4 Boolean Classifiers 27.5 Series Methods for the Hypercube 27.6 Maximum Likelihood 27.7 Kernel Methods Problems and Exercises 461 461 464 466 468 470 472 474 474 28 Epsilon Entropy and Totally Bounded Sets 28.1 Definitions 28.2 Examples: Totally Bounded Classes 28.3 Skeleton Estimates 28.4 Rate of Convergence Problems and Exercises 479 479 480 482 485 486 29 Uniform Laws of Large Numbers 29.1 Minimizing the Empirical Squared Error 29.2 Uniform Deviations of Averages from Expectations 29.3 Empirical Squared Error Minimization 29.4 Proof of Theorem 29.1 29.5 Covering Numbers and Shatter Coefficients 29.6 Generalized Linear Classification Problems and Exercises 489 489 490 493 494 496 501 505 30 Neural Networks 30.1 Multilayer Perceptrons 30.2 Arrangements 507 507 511
Contents 30.3 Approximation by Neural Networks 30.4 VC Dimension 30.5 L| Error Minimization 30.6 The Adaline and Padaline 30.7 Polynomial Networks 30.8 Kolmogorov-Lorentz Networks and Additive Models 30.9 Projection Pursuit 30.10 Radial Basis Function Networks Problems and Exercises XV 517 521 526 531 532 534 538 540 542 31 Other Error Estimates 31.1 Smoothing the Error Count 31.2 Posterior Probability Estimates 31.3 Rotation Estimate 31.4 Bootstrap Problems and Exercises 549 549 554 556 556 559 32 Feature Extraction 32.1 Dimensionality Reduction 32.2 Transformations with Small Distortion 32.3 Admissible and Sufficient Transformations Problems and Exercises 561 561 567 569 572 Appendix A.l A.2 A.3 A.4 A.5 A.6 A.7 A.8 A.9 A. 10 A. 11 A. 12 575 575 576 579 581 582 584 585 586 589 589 590 590 Basics of Measure Theory The Lebesgue Integral Denseness Results Probability Inequalities Convergence of Random Variables Conditional Expectation The Binomial Distribution The Hypergeometric Distribution The Multinomial Distribution The Exponential and Gamma Distributions The Multivariate Normal Distribution Notation 591 References 593 Author Index 619 Subject Index 627 |
| any_adam_object | 1 |
| author | Devroye, Luc Györfi, László Lugosi, Gábor 1964- |
| author_GND | (DE-588)170228444 (DE-588)1023925419 (DE-588)17173677X |
| author_facet | Devroye, Luc Györfi, László Lugosi, Gábor 1964- |
| author_role | aut aut aut |
| author_sort | Devroye, Luc |
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| building | Verbundindex |
| bvnumber | BV010783997 |
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| callnumber-label | Q327 |
| callnumber-raw | Q327.D5 1996 |
| callnumber-search | Q327.D5 1996 |
| callnumber-sort | Q 3327 D5 41996 |
| callnumber-subject | Q - General Science |
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| classification_tum | MAT 600f DAT 770f |
| ctrlnum | (OCoLC)33276839 (DE-599)BVBBV010783997 |
| dewey-full | 003/.52/01519220 003/.52/015192 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.52/015192 20 003/.52/015192 |
| dewey-search | 003/.52/015192 20 003/.52/015192 |
| dewey-sort | 13 252 515192 220 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV010783997 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-07T11:02:23Z |
| institution | BVB |
| isbn | 0387946187 9780387946184 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007202967 |
| oclc_num | 33276839 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-12 DE-29T DE-19 DE-BY-UBM DE-739 DE-703 DE-824 DE-355 DE-BY-UBR DE-20 DE-384 DE-1051 DE-521 DE-634 DE-83 DE-188 DE-N2 |
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| physical | XV, 636 S. Diagramme |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Devroye, Luc Verfasser (DE-588)170228444 aut A probabilistic theory of pattern recognition Luc Devroye ; László Györfi ; Gábor Lugosi New York [u.a.] Springer 1996 XV, 636 S. Diagramme txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 31 Pattern recognition presents one of the most significant challenges for scientists and engineers, and many different approaches have been proposed. The aim of this book is to provide a self-contained account of probabilistic analysis of these approaches. The book includes a discussion of distance measures, nonparametric methods based on kernels or nearest neighbors, Vapnik-Chervonenkis theory, epsilon entropy, parametric classification, error estimation, tree classifiers, and neural networks Wherever possible, distribution-free properties and inequalities are derived. A substantial portion of the results or the analysis is new. Over 430 problems and exercises complement the material Inteligência artificial larpcal Patroonherkenning gtt Perception des structures Perception des structures ram Probabilités Probabilités ram Reconhecimento de padrões larpcal Waarschijnlijkheidstheorie gtt Pattern perception Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Mustererkennung (DE-588)4040936-3 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Mustererkennung (DE-588)4040936-3 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 2\p DE-604 Györfi, László Verfasser (DE-588)1023925419 aut Lugosi, Gábor 1964- Verfasser (DE-588)17173677X aut Applications of mathematics 31 (DE-604)BV000895226 31 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007202967&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Devroye, Luc Györfi, László Lugosi, Gábor 1964- A probabilistic theory of pattern recognition Applications of mathematics Inteligência artificial larpcal Patroonherkenning gtt Perception des structures Perception des structures ram Probabilités Probabilités ram Reconhecimento de padrões larpcal Waarschijnlijkheidstheorie gtt Pattern perception Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Mustererkennung (DE-588)4040936-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4040936-3 (DE-588)4064324-4 (DE-588)4143389-0 |
| title | A probabilistic theory of pattern recognition |
| title_auth | A probabilistic theory of pattern recognition |
| title_exact_search | A probabilistic theory of pattern recognition |
| title_full | A probabilistic theory of pattern recognition Luc Devroye ; László Györfi ; Gábor Lugosi |
| title_fullStr | A probabilistic theory of pattern recognition Luc Devroye ; László Györfi ; Gábor Lugosi |
| title_full_unstemmed | A probabilistic theory of pattern recognition Luc Devroye ; László Györfi ; Gábor Lugosi |
| title_short | A probabilistic theory of pattern recognition |
| title_sort | a probabilistic theory of pattern recognition |
| topic | Inteligência artificial larpcal Patroonherkenning gtt Perception des structures Perception des structures ram Probabilités Probabilités ram Reconhecimento de padrões larpcal Waarschijnlijkheidstheorie gtt Pattern perception Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Mustererkennung (DE-588)4040936-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Inteligência artificial Patroonherkenning Perception des structures Probabilités Reconhecimento de padrões Waarschijnlijkheidstheorie Pattern perception Probabilities Wahrscheinlichkeitstheorie Mustererkennung Wahrscheinlichkeitsrechnung Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007202967&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
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