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Kernel Methods for Pattern Analysis

Book Description

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 neural networks and pattern recognition to machine learning and data mining. This book, developed from lectures and tutorials, fulfils two major roles: firstly it provides practitioners with a large toolkit of algorithms, kernels and solutions ready to use for standard pattern discovery problems in fields such as bioinformatics, text analysis, image analysis. Secondly it provides an easy introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new specific application, and covering all the necessary conceptual and mathematical tools to do so.

Table of Contents

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