Optimization techniques have been widely adopted to implement various data mining algorithms. In addition to well-known Support Vector Machines (SVMs) (which are based on quadratic programming), different versions of Multiple Criteria Programming (MCP) have been extensively used in data separations. Since optimization based data mining methods differ from statistics, decision tree induction, and neural networks, their theoretical inspiration has attracted many researchers who are interested in algorithm development of data mining. Optimization based Data Mining: Theory and Applications, mainly. Read more...
Abstract:
Optimization techniques have been widely adopted to implement various data mining algorithms. This book focuses on cutting-edge theoretical developments and real-life applications in optimization, covering a range of fields from finance to bioinformatics. Read more...
Author(s): Kou, Gang; Li, Jianping; Peng, Yi; Shi, Yong; Tian, Yingjie et al.
Series: Advanced information and knowledge processing
Publisher: Springer London
Year: 2011
Language: English
Pages: 313
Tags: Data mining.
Content: Optimization Based Data Mining: Theory and Applications
Preface
Contents
Part I: Support Vector Machines: Theory and Algorithms
Chapter 1: Support Vector Machines for Classification Problems
1.1 Method of Maximum Margin
1.2 Dual Problem
1.3 Soft Margin
1.4 C-Support Vector Classification
1.5 C-Support Vector Classification with Nominal Attributes
1.5.1 From Fixed Points to Flexible Points
1.5.2 C-SVC with Nominal Attributes
1.5.3 Numerical Experiments
Chapter 2: LOO Bounds for Support Vector Machines
2.1 Introduction
2.2 LOO Bounds for epsilon-Support Vector Regression. 2.2.1 Standard epsilon-Support Vector Regression2.2.2 The First LOO Bound
2.2.3 A Variation of epsilon-Support Vector Regression
2.2.4 The Second LOO Bound
2.2.5 Numerical Experiments
2.3 LOO Bounds for Support Vector Ordinal Regression Machine
2.3.1 Support Vector Ordinal Regression Machine
2.3.2 The First LOO Bound
Definition and Existence of Span
The Bound
2.3.3 The Second LOO Bound
2.3.4 Numerical Experiments
Chapter 3: Support Vector Machines for Multi-class Classification Problems
3.1 K-Class Linear Programming Support Vector Classification Regression Machine (K-LPSVCR). 3.1.1 K-LPSVCR3.1.2 Numerical Experiments
Experiments on Artificial Data Sets
Experiments on Benchmark Data Sets
3.1.3 nu-K-LPSVCR
3.2 Support Vector Ordinal Regression Machine for Multi-class Problems
3.2.1 Kernel Ordinal Regression for 3-Class Problems
3.2.2 Multi-class Classification Algorithm
3.2.3 Numerical Experiments
Example in the Plane
Experiments on Benchmark Data Sets
Chapter 4: Unsupervised and Semi-supervised Support Vector Machines
4.1 Unsupervised and Semi-supervised nu-Support Vector Machine
4.1.1 Bounded nu-Support Vector Machine. 4.1.2 nu-SDP for Unsupervised Classification Problems4.1.3 nu-SDP for Semi-supervised Classification Problems
4.2 Numerical Experiments
4.2.1 Numerical Experiments of Algorithm 4.2
4.2.2 Numerical Experiments of Algorithm 4.3
4.3 Unsupervised and Semi-supervised Lagrange Support Vector Machine
4.4 Unconstrained Transductive Support Vector Machine
4.4.1 Transductive Support Vector Machine
4.4.2 Unconstrained Transductive Support Vector Machine
Unconstrained Optimization Problem
Smooth Unconstrained Optimization Problem. 4.4.3 Unconstrained Transductive Support Vector Machine with KernelsChapter 5: Robust Support Vector Machines
5.1 Robust Support Vector Ordinal Regression Machine
5.2 Robust Multi-class Algorithm
5.3 Numerical Experiments
5.3.1 Numerical Experiments of Algorithm 5.6
5.3.2 Numerical Experiments of Algorithm 5.7
5.4 Robust Unsupervised and Semi-supervised Bounded C-Support Vector Machine
5.4.1 Robust Linear Optimization
5.4.2 Robust Algorithms with Polyhedron
5.4.3 Robust Algorithm with Ellipsoid
5.4.4 Numerical Results
Chapter 6: Feature Selection via lp-Norm Support Vector Machines.
