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内容大纲
模式分析是从一批数据中寻找普遍关系的过程。它逐渐成为许多学科的核心,从生物信息学到文档检索都有广泛需求。本书所描述的核方法为所有这些学科提供了一个有力的和统一的框架,推动了可以用于各种普遍形式的数据(如字符串、向量、文本等)的各种算法的发展,并可以用于寻找各种普遍的关系类型(如排序、分类、回归和聚类等)。书中提供了大量算法、核函数和具体解决方案供各种实际问题选择使用。书中描述了各种核函数,从基本的例子到高等递归核函数,从生成模型导出的核函数(如HMM)到基于动态规划的串匹配核函数,以及用于处理文本文档的特殊核函数等。本书适用于所有从事人工智能、模式识别、机器学习、神经网络及其应用的学生、教师和研究人员,也可供相关领域的科研人员参考。 -
作者介绍
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目录
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 fleature 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 Vactor 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-subseauences 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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