Kernels for structured data

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....

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Bibliographic Details
Main Author: Gartner, Thomas
Format: eBook Book
Language:English
Published: New Jersey World Scientific Publishing Co. Pte. Ltd 2008
World Scientific
World Scientific Publishing Company
WORLD SCIENTIFIC
World Scientific Publishing
Edition:1
Series:Series in machine perception and artificial intelligence
Subjects:
Artificial Intelligence (Machine Learning, Neural Networks, Fuzzy Logic)
Computer Systems (Database Systems, Operating Systems)
Kernel functions
Machine learning
Robotics (Machine Vision, Pattern Recognition)
SCIENCE
Kernel Methods
Graph Kernels
Machine Learning
Relational Learning
Structured Data
ISBN:9812814558, 9789812814555, 9789812814562, 9812814566
Online Access:Get full text
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Table of Contents:
  • Kernels for structured data -- Preface -- Contents -- Notational Conventions -- Chapter 1: Why Kernels for Structured Data? -- Chapter 2: Kernel Methods in a Nutshell -- Chapter 3: Kernel Design -- Chapter 4: Basic Term Kernels -- Chapter 5: Graph Kernels -- Chapter 6: Conclusions -- Bibliography -- Index.
  • 5.7.4.2 Comparison with previous RRL-implementations -- 5.7.5 Future Work -- 5.8 Molecule Classification -- 5.8.1 Mutagenicity -- 5.8.2 HIV Data -- 5.9 Summary -- 6. Conclusions -- Bibliography -- Index
  • Intro -- Contents -- Preface -- 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 Crossproduct 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 -- 5.4.2 Kernels Based on Contiguous Label Sequences -- 5.4.3 Transition Graphs -- 5.4.4 Non-Contiguous Label Sequences -- 5.5 Cyclic Pattern Kernels -- 5.5.1 Undirected Graphs -- 5.5.2 Kernel Definition -- 5.5.3 Kernel Computation -- 5.6 Related Work -- 5.7 Relational Reinforcement Learning -- 5.7.1 Relational Reinforcement Learning -- 5.7.2 Kernels for Graphs with Parallel Edges -- 5.7.3 Kernel Based RRL in the Blocks World -- 5.7.3.1 State and Action Representation -- 5.7.3.2 Blocks World Kernels -- 5.7.4 Experiments -- 5.7.4.1 Parameter Influence