List of code fragments
Preface
Part I Basic concepts
1 Pattern analysis
1.1 Patterns in data
1.2 Pattern analysis algorithms
1.3 Exploiting patterns
1.4 Summary
1.5 Further reading and advanced topics
2 Kernel methods: an overview
2.1 The overall picture
2.2 Linear regression in a feature space
2.3 Other examples
2.4 The modularity of kernel methods
2.5 Roadmap of the book
2.6 Summary
2.7 Further reading and advanced topics
3 Properties of kernels
3.1 Inner products and positive semi-definite matrices
3.2 Characterisation of kernels
3.3 The kernel matrix
3.4 Kernel construction
3.5 Summary
3.6 Further reading and advanced topics
4 Detecting stable patterns
4.1 Concentration inequalities
4.2 Capacity and regularisation: Rademacher theory
4.3 Pattern stability for kernel-based classes
4.4 A pragmatic approach
4.5 Summary
4.6 Further reading and advanced topics
Part II Pattern analysis algorithms
5 Elementary algorithms in feature space
5.1 Means and distances
5.2 Computing projections: Gram-Schmidt, QR and Cholesky
5.3 Measuring the spread of the data
5.4 Fisher discriminant analysis I
5.5 Summary
5.6 Further reading and advanced topics
6 Pattern analysis using eigen-decompositions
6.1 Singular value decomposition
6.2 Principal components analysis
6.3 Directions of maximum covariance
6.4 The generalised eigenvector problem
6.5 Canonical correlation analysis
6.6 Fisher discriminant analysis II
6.7 Methods for linear regression
6.8 Summary
6.9 Further reading and advanced topics
7 Pattern analysis using convex optimisation
7.1 The smallest enclosing hypersphere
7.2 Support vector machines for classification
7.3 Support vector machines for regression
7.4 On-line classification and regression
7.5 Summary
7.6 Further reading and advanced topics
8 Ranking, clustering and data visualisation
8.1 Discovering rank relations
8.2 Discovering cluster structure in a feature space
8.3 Data visualisation
8.4 Summary
8.5 Further reading and advanced topics
Part III Constructing kernels
9 Basic kernels and kernel types
9.1 Kernels in closed form
9.2 ANOVA kernels
9.3 Kernels from graphs
9.4 Diffusion kernels on graph nodes
9.5 Kernels on sets
9.6 Kernels on real numbers
9.7 Randomised kernels
9.8 Other kernel types
9.9 Summary
9.10 Further reading and advanced topics
10 Kernels for text
10.1 From bag of words to semantic space
10.2 Vector space kernels
10.3 Summary
10.4 Further reading and advanced topics
11 Kernels for structured data: strings, trees, etc.
11.1 Comparing strings and sequences
11.2 Spectrum kernels
11.3 All-subsequences kernels
11.4 Fixed length subsequences kernels
11.5 Gap-weighted subsequences kernels
11.6 Beyond dynamic programming: trie-based kernels
11.7 Kernels for structured data
11.8 Summary
11.9 Further reading and advanced topics
12 Kernels from generative models
12.1 P-kernels
12.2 Fisher kernels
12.3 Summary
12.4 Further reading and advanced topics
Appendix A Proofs omitted from the main text
Appendix B Notational conventions
Appendix C List of pattern analysis methods
Appendix D List of kernels
References
Index
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