book

Pattern Recognition

Name: Pattern Recognition
ISBN: 9783110537963

by Jürgen Beyerer, Matthias Richter, Matthias Nagel

December 2017

Beginner to intermediate

311 pages

11h 26m

English

De Gruyter Oldenbourg

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Cover
Title Page
Copyright
Preface
Contents
List of Tables
List of Figures
Notation
Introduction
1 Fundamentals and definitions
1.1 Goals of pattern recognition1.2 Structure of a pattern recognition system1.3 Abstract view of pattern recognition1.4 Design of a pattern recognition system1.5 Exercises

2 Features
2.1 Types of features and their traits2.1.1 Nominal scale2.1.2 Ordinal scale2.1.3 Interval scale2.1.4 Ratio scale and absolute scale2.2 Feature space inspection2.2.1 Projections2.2.2 Intersections and slices2.3 Transformations of the feature space2.4 Measurement of distances in the feature space2.4.1 Basic definitions2.4.2 Elementary norms and metrics2.4.3 A metric for sets2.4.4 Metrics on the ordinal scale2.4.5 The Kullback–Leibler divergence
2.4.6 Tangential distance measure
2.5 Normalization2.5.1 Alignment, elimination of physical dimension, and leveling of proportions2.5.2 Lighting adjustment of images
2.5.3 Distortion adjustment of images
2.5.4 Dynamic time warping2.6 Selection and construction of features2.6.1 Descriptive features2.6.2 Model-driven features
2.6.3 Construction of invariant features
2.7 Dimensionality reduction of the feature space
2.7.1 Principal component analysis
2.7.2 Kernelized principal component analysis
2.7.3 Independent component analysis
2.7.4 Multiple discriminant analysis
2.7.5 Dimensionality reduction by feature selection
2.7.6 Bag of words2.8 Exercises
3 Bayesian decision theory
3.1 General considerations3.2 The maximum a posteriori classifier3.3 Bayesian classification3.3.1 The Bayesian optimal classifier
3.3.2 Reference example: Optimal decision regions
3.3.3 The minimax classifier3.3.4 Normally distributed features
3.3.5 Arbitrarily distributed features
3.4 Exercises
4 Parameter estimation
4.1 Maximum likelihood estimation
4.2 Bayesian estimation of the class-specific distributions
4.3 Bayesian parameter estimation
4.3.1 Least squared estimation error4.3.2 Constant penalty for failures4.4 Additional remarks on Bayesian classification4.5 Exercises
5 Parameter free methods
5.1 The Parzen window method5.2 The k-nearest neighbor method5.3 k-nearest neighbor classification5.4 Exercises
6 General considerations
6.1 Dimensionality of the feature space6.2 Overfitting6.3 Exercises
7 Special classifiers
7.1 Linear discriminants7.1.1 More than two classes7.1.2 Nonlinear separation7.2 The perceptron7.3 Linear regression7.4 Artificial neural networks7.5 Autoencoders7.6 Deep learning7.6.1 Historical difficulties and successful approaches7.6.2 Unsupervised pre-training
7.6.3 Stochastic gradient descent
7.6.4 Rectified linear units7.6.5 Convolutional neural networks7.7 Support vector machines7.7.1 Linear separation with maximum margin7.7.2 Dual formulation7.7.3 Nonlinear mapping7.7.4 The kernel trick
7.7.5 No linear separability
7.7.6 Discussion7.8 Matched filters
7.9 Classification of sequences
7.9.1 Markov models7.9.2 Hidden states7.10 Exercises
8 Classification with nominal features
8.1 Decision trees8.1.1 Decision tree learning8.1.2 Influence of the features used8.2 Random forests8.3 String matching8.4 Grammars8.5 Exercises
9 Classifier-independent concepts
9.1 Learning theory9.1.1 The central problem of statistical learning9.1.2 Vapnik–Chervonenkis learning theory9.2 Empirical evaluation of classifier performance9.2.1 Receiver operating characteristic9.2.2 Multi-class setting9.2.3 Theoretical bounds with finite test sets9.2.4 Dealing with small datasets9.3 Boosting9.4 Rejection9.5 Exercises
A Solutions to the exercises
A.1 Chapter 1A.2 Chapter 2A.3 Chapter 3A.4 Chapter 4
A.5 Chapter 5
A.6 Chapter 6A.7 Chapter 7A.8 Chapter 8A.9 Chapter 9
B A primer on Lie theory
C Random processes
Bibliography
Glossary
Index

Content preview from Pattern Recognition

BA primer on Lie theory

The tangential distance in Section 2.4.6 as well as the construction of invariant features in Section 2.6.3 used concepts from Lie theory, but gave no formal introduction of these concepts. This section will give a concise introduction to the postponed mathematical details.

Definition B.1 (Topological Manifold). Let Π be a Hausdorff space, i. e., a set of points with a system of open sets such that for each pair of two distinct points the points can be placed in two disjoint open sets.

1.A chart (or coordinate chart or coordinate map) is a pair (U, φ) of an open subset U ⊆Π and a corresponding injective map φ: U → V to an open subset V ⊆ d of Euclidean space such that φ is a homeomorphism. To be a homeomorphism means ...

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Pattern Recognition

by Jürgen Beyerer, Matthias Richter, Matthias Nagel

BA primer on Lie theory

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.