Kernels for structured data / Thomas Gartner.

Format:

Book

Author/Creator:

Gärtner, Thomas.

Series:

Series in Machine Perception and Artificial Intelligence

Series in machine perception and artificial intelligence ; v. 72

Language:

English

Subjects (All):

Machine learning.

Kernel functions.

Physical Description:

1 online resource (216 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2008.

Language Note:

English

Summary:

This book provides a unique treatment of an important area of machine learning and answers the question of how kernel methods can be applied to structured data. Kernel methods are a class of state-of-the-art learning algorithms that exhibit excellent learning results in several application domains. Originally, kernel methods were developed with data in mind that can easily be embedded in a Euclidean vector space. Much real-world data does not have this property but is inherently structured. An example of such data, often consulted in the book, is the (2D) graph structure of molecules formed by

Contents:

Preface; Contents; Notational Conventions; 1. Why Kernels for Structured Data?; 1.1 Supervised Machine Learning; 1.2 Kernel Methods; 1.3 Representing Structured Data; 1.4 Goals and Contributions; 1.5 Outline; 1.6 Bibliographical Notes; 2. Kernel Methods in a Nutshell; 2.1 Mathematical Foundations; 2.1.1 From Sets to Functions; 2.1.2 Measures and Integrals; 2.1.3 Metric Spaces; 2.1.4 Linear Spaces and Banach Spaces; 2.1.5 Inner Product Spaces and Hilbert Spaces; 2.1.6 Reproducing Kernels and Positive-Definite Functions; 2.1.7 Matrix Computations; 2.1.8 Partitioned Inverse Equations

2.2 Recognising Patterns with Kernels 2.2.1 Supervised Learning; 2.2.2 Empirical Risk Minimisation; 2.2.3 Assessing Predictive Performance; 2.3 Foundations of Kernel Methods; 2.3.1 Model Fitting and Linear Inverse Equations; 2.3.2 Common Grounds of Kernel Methods; 2.3.3 Representer Theorem; 2.4 Kernel Machines; 2.4.1 Regularised Least Squares; 2.4.2 Support Vector Machines; 2.4.3 Gaussian Processes; 2.4.4 Kernel Perceptron; 2.4.5 Kernel Principal Component Analysis; 2.4.6 Distance-Based Algorithms; 2.5 Summary; 3. Kernel Design; 3.1 General Remarks on Kernels and Examples

3.1.1 Classes of Kernels 3.1.2 Good Kernels; 3.1.3 Kernels on Inner Product Spaces; 3.1.4 Some Illustrations; 3.2 Kernel Functions; 3.2.1 Closure Properties; 3.2.2 Kernel Modifiers; 3.2.3 Minimal and Maximal Functions; 3.2.4 Soft-Maximal Kernels; 3.3 Introduction to Kernels for Structured Data; 3.3.1 Intersection and Cross product Kernels on Sets; 3.3.2 Minimal and Maximal Functions on Sets; 3.3.3 Kernels on Multisets; 3.3.4 Convolution Kernels; 3.4 Prior Work; 3.4.1 Kernels from Generative Models; 3.4.2 Kernels from Instance Space Graphs; 3.4.3 String Kernels; 3.4.4 Tree Kernels; 3.5 Summary

4. Basic Term Kernels 4.1 Logics for Learning; 4.1.1 Propositional Logic for Learning; 4.1.2 First-Order Logic for Learning; 4.1.3 Lambda Calculus; 4.1.4 Lambda Calculus with Polymorphic Types; 4.1.5 Basic Terms for Learning; 4.2 Kernels for Basic Terms; 4.2.1 Default Kernels for Basic Terms; 4.2.2 Positive Definiteness of the Default Kernel; 4.2.2 Positive Definiteness of the Default Kernel . . . . 98 4.2.3 Specifying Kernels; 4.3 Multi-Instance Learning; 4.3.1 The Multi-Instance Setting; 4.3.2 Separating MI Problems; 4.3.3 Convergence of the MI Kernel Perceptron; 4.3.4 Alternative MI Kernels

4.3.5 Learning MI Ray Concepts 4.4 Related Work; 4.4.1 Kernels for General Data Structures; 4.4.2 Multi-Instance Learning; 4.5 Applications and Experiments; 4.5.1 East/West Challenge; 4.5.2 Drug Activity Prediction; 4.5.3 Structure Elucidation from Spectroscopic Analyses; 4.5.4 Spatial Clustering; 4.6 Summary; 5. Graph Kernels; 5.1 Motivation and Approach; 5.2 Labelled Directed Graphs; 5.2.1 Basic Terminology and Notation; 5.2.2 Matrix Notation and some Functions; 5.2.3 Product Graphs; 5.2.4 Limits of Matrix Power Series; 5.3 Complete Graph Kernels; 5.4 Walk Kernels

5.4.1 Kernels Based on Label Pairs

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 179-190) and index.

ISBN:

9789812814562

9812814566

OCLC:

820944529