Support Vector Machines

Optimization Based Theory, Algorithms, and Extensions

; Yingjie Tian ; Chunhua Zhang

Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents an accessible treatment of the two main components of support vector machines (SVMs)-classification problems and regression problems. Les mer
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Om boka

Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents an accessible treatment of the two main components of support vector machines (SVMs)-classification problems and regression problems. The book emphasizes the close connection between optimization theory and SVMs since optimization is one of the pillars on which SVMs are built.





The authors share insight on many of their research achievements. They give a precise interpretation of statistical leaning theory for C-support vector classification. They also discuss regularized twin SVMs for binary classification problems, SVMs for solving multi-classification problems based on ordinal regression, SVMs for semi-supervised problems, and SVMs for problems with perturbations.





To improve readability, concepts, methods, and results are introduced graphically and with clear explanations. For important concepts and algorithms, such as the Crammer-Singer SVM for multi-class classification problems, the text provides geometric interpretations that are not depicted in current literature.





Enabling a sound understanding of SVMs, this book gives beginners as well as more experienced researchers and engineers the tools to solve real-world problems using SVMs.

Fakta

Innholdsfortegnelse

Optimization
Optimization Problems in Euclidian Space
Convex Programming in Euclidean Space
Convex Programming in Hilbert Space
Convex Programming with Generalized Inequality Constraints in Rn
Convex Programming with Generalized Inequality Constraints in Hilbert Space





Linear Classification Machines
Presentation of Classification Problems
Support Vector Classification (SVC) for Linearly Separable Problems
Linear Support Vector Classification





Linear Regression Machines
Regression Problems and Linear Regression Problems
Hard -Band Hyperplane
Linear Hard -Band Support Vector Regression
Linear -Support Vector Regression





Kernels and Support Vector Machines
From Linear Classification to Nonlinear Classification
Kernels
Support Vector Machines and Their Properties
Meaning of Kernels





Basic Statistical Learning Theory of C-Support Vector Classification
Classification Problems on Statistical Learning Theory
Empirical Risk Minimization
Vapnik Chervonenkis (VC) Dimension
Structural Risk Minimization
An Implementation of Structural Risk Minimization
Theoretical Foundation of C-Support Vector Classification on Statistical Learning Theory





Model Construction
Data Generation
Data Preprocessing
Model Selection
Rule Extraction





Implementation
Stopping Criterion
Chunking
Decomposing
Sequential Minimal Optimization
Software





Variants and Extensions of Support Vector Machines
Variants of Binary Classification
Variants of Regression
Multi-Class Classification
Semi-Supervised Classification
Universum Classification
Privileged Classification
Knowledge-Based Classification
Robust Classification
Multi-Instance Classification
Multi-Label Classification


Bibliography


Index