Kernel Methods for Pattern Analysis
Kernel methods provide a powerful and unified framework for pattern discovery, motivating algorithms that can act on general types of data (e.g. strings, vectors or text) and look for general types of relations (e.g. rankings, classifications, regressions, clusters). The application areas range from...
Uloženo v:
| Hlavní autoři: | , |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cambridge
Cambridge University Press
28.06.2004
|
| Vydání: | 1 |
| Témata: | |
| ISBN: | 9780521813976, 0521813972 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
Obsah:
- 9.8.1 Kernels from successive embeddings -- 9.8.2 Kernels over general structures -- 9.8.3 Kernels from generative information -- 9.9 Summary -- 9.10 Further reading and advanced topics -- 10 Kernels for text -- 10.1 From bag of words to semantic space -- 10.1.1 Representing text -- 10.1.2 Semantic issues -- 10.2 Vector space kernels -- 10.2.1 Designing semantic kernels -- 10.2.2 Designing the proximity matrix -- 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 -- 11.5.1 Naive implementation -- 11.5.2 Efficient implementation -- 11.5.3 Variations on the theme -- 11.6 Beyond dynamic programming: trie-based kernels -- 11.6.1 Trie computation of the p-spectrum kernels -- 11.6.2 Trie-based mismatch kernels -- 11.6.3 Trie-based restricted gap-weighted kernels -- 11.7 Kernels for structured data -- 11.7.1 Comparing trees -- 11.7.2 Structured data: a framework -- 11.8 Summary -- 11.9 Further reading and advanced topics -- 12 Kernels from generative models -- 12.1 P-kernels -- 12.1.1 Conditional-independence (CI) and marginalisation -- 12.1.2 Representing multivariate distributions -- 12.1.3 Fixed length strings generated by a hidden binomial model -- 12.1.4 Fixed length strings generated by a hidden markov model -- 12.1.5 Pair hidden Markov model kernels -- 12.1.6 Hidden tree model kernels -- 12.2 Fisher kernels -- 12.2.1 From probability to geometry -- 12.2.2 Fisher kernels for hidden Markov models -- 12.3 Summary -- 12.4 Further reading and advanced topics -- Appendix A Proofs omitted from the main text -- A.1 Proof of McDiarmid's theorem -- A.2 Stability of principal components analysis
- 5.6 Further reading and advanced topics -- 6 Pattern analysis using eigen-decompositions -- 6.1 Singular value decomposition -- 6.2 Principal components analysis -- 6.2.1 Kernel principal components analysis -- 6.2.2 Stability of 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 -- 6.7.1 Partial least squares -- 6.7.2 Kernel partial least squares -- 6.8 Summary -- 6.9 Further reading and advanced topics -- 7 Pattern analysis using convex optimisation -- 7.1 The smallest enclosing hypersphere -- 7.1.1 The smallest hypersphere containing a set of points -- 7.1.2 Stability of novelty-detection -- 7.1.3 Hyperspheres containing most of the points -- 7.2 Support vector machines for classification -- 7.2.1 The maximal margin classifier -- 7.2.2 Soft margin classifiers -- 7.3 Support vector machines for regression -- 7.3.1 Stability of regression -- 7.3.2 Ridge regression -- 7.3.3 ε-insensitive 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 -- 8.1.1 Batch ranking -- 8.1.2 On-line ranking -- 8.2 Discovering cluster structure in a feature space -- 8.2.1 Measuring cluster quality -- 8.2.2 Greedy solution: k-means -- 8.2.3 Relaxed solution: spectral methods -- 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
- A.3 Proofs of diffusion kernels -- Appendix B Notational conventions -- B.1 List of symbols -- B.2 Notation for Tables -- Appendix C List of pattern analysis methods -- C.1 Pattern analysis computations -- C.2 Pattern analysis algorithms -- Appendix D List of kernels -- D.1 Kernel definitions and computations -- D.2 Kernel algorithms -- References -- Index
- Cover -- Half-title -- Title -- Copyright -- Contents -- Code fragments -- Preface -- Part I Basic concepts -- 1 Pattern analysis -- 1.1 Patterns in data -- 1.1.1 Data -- 1.1.2 Patterns -- 1.2 Pattern analysis algorithms -- 1.2.1 Statistical stability of patterns -- 1.2.2 Detecting patterns by recoding -- 1.3 Exploiting patterns -- 1.3.1 The overall strategy -- 1.3.2 Common pattern analysis tasks -- 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 -- 2.2.1 Primal linear regression -- 2.2.2 Ridge regression: primal and dual -- 2.2.3 Kernel-defined nonlinear feature mappings -- 2.3 Other examples -- 2.3.1 Algorithms -- 2.3.2 Kernels -- 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 -- 3.1.1 Hilbert spaces -- 3.1.2 Gram matrix -- 3.2 Characterisation of kernels -- 3.3 The kernel matrix -- 3.4 Kernel construction -- 3.4.1 Operations on kernel functions -- 3.4.2 Operations on kernel matrices -- 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 -- 5.1.1 A simple algorithm for novelty-detection -- 5.1.2 A simple algorithm for classification -- 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