A probabilistic theory of pattern recognition /
Devroye, Luc.
A probabilistic theory of pattern recognition / Luc Devroye, László Györfi, Gábor Lugosi. - New Delhi : Springer, CBS Publishers, 2014, c1996. - xv, 636 p. : ill. ; 25 cm. - Applications of mathematics ; 31 . - Applications of mathematics ; 31. .
Includes bibliographical references (p. [593]-618) and indexes.
Introduction -- The Bayes Error -- Inequalities and Alternate Distance Measures -- Linear Discrimination -- Nearest Neighbor Rules -- Consistency -- Slow Rates of Convergence -- Error Estimation -- The Regular Histogram Rule -- Kernel Rules -- Consistency of the k-Nearest Neighbor Rule -- Vapnik-Chervonenkis Theory -- Combinatorial Aspects of Vapnik-Chervonenkis Theory -- Lower Bounds for Empirical Classifier Selection -- The Maximum Likelihood Principle -- Parametric Classification -- Generalized Linear Discrimination -- Complexity Regularization -- Condensed and Edited Nearest Neighbor Rules -- Tree Classifiers -- Data-Dependent Partitioning -- Splitting the Data -- The Resubstitution Estimate -- Deleted Estimates of the Error Probability -- Automatic Kernel Rules -- Automatic Nearest Neighbor Rules -- Hypercubes and Discrete Spaces -- 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Epsilon Entropy and Totally Bounded Sets -- Uniform Laws of Large Numbers -- Neural Networks -- Other Error Estimates -- Feature Extraction. 28. 29. 30. 31. 32.
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.
9788132214977
Pattern perception.
Probabilities.
Q327 / .D5 1996
003.52015192 / DEV
A probabilistic theory of pattern recognition / Luc Devroye, László Györfi, Gábor Lugosi. - New Delhi : Springer, CBS Publishers, 2014, c1996. - xv, 636 p. : ill. ; 25 cm. - Applications of mathematics ; 31 . - Applications of mathematics ; 31. .
Includes bibliographical references (p. [593]-618) and indexes.
Introduction -- The Bayes Error -- Inequalities and Alternate Distance Measures -- Linear Discrimination -- Nearest Neighbor Rules -- Consistency -- Slow Rates of Convergence -- Error Estimation -- The Regular Histogram Rule -- Kernel Rules -- Consistency of the k-Nearest Neighbor Rule -- Vapnik-Chervonenkis Theory -- Combinatorial Aspects of Vapnik-Chervonenkis Theory -- Lower Bounds for Empirical Classifier Selection -- The Maximum Likelihood Principle -- Parametric Classification -- Generalized Linear Discrimination -- Complexity Regularization -- Condensed and Edited Nearest Neighbor Rules -- Tree Classifiers -- Data-Dependent Partitioning -- Splitting the Data -- The Resubstitution Estimate -- Deleted Estimates of the Error Probability -- Automatic Kernel Rules -- Automatic Nearest Neighbor Rules -- Hypercubes and Discrete Spaces -- 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. Epsilon Entropy and Totally Bounded Sets -- Uniform Laws of Large Numbers -- Neural Networks -- Other Error Estimates -- Feature Extraction. 28. 29. 30. 31. 32.
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.
9788132214977
Pattern perception.
Probabilities.
Q327 / .D5 1996
003.52015192 / DEV