Support vector machines : optimization based theory, algorithms, and extensions

✍ Scribed by Naiyang Deng; Yingjie Tian; Chunhua Zhang

• Publisher: CRC Press Taylor & Francis Group
• Tongue: English
• Leaves: 345
• Series: Chapman & Hall/CRC data mining and knowledge discovery series
• Category: Library

✦ Synopsis

''Preface Support vector machines (SVMs), which were introduced by Vapnik in the early 1990s, are proved effective and promising techniques for data mining. SVMs have recently been breakthroughs in advance in their theoretical studies and implementations of algorithms. They have been successfully applied in many fields such as text categorization, speech recognition, remote sensing image analysis, time series forecasting, information security and etc. SVMs, having their roots in Statistical Learning Theory (SLT) and optimization methods, become powerful tools to solve the problems of machine learning with finite training points and to overcome some traditional difficulties such as the ''curse of dimensionality'', ''over-fitting'' and etc. SVMs theoretical foundation and implementation techniques have been established and SVMs are gaining quick development and popularity due to their many attractive features: nice mathematical representations, geometrical explanations, good generalization abilities and promising empirical performance. Some SVM monographs, including more sophisticated ones such as Cristianini & Shawe-Taylor [39] and Scholkopf & Smola [124], have been published. We have published two books about SVMs in Science Press of China since 2004 [42, 43], which attracted widespread concerns and received favorable comments. After several years research and teaching, we decide to rewrite the books and add new research achievements. The starting point and focus of the book is optimization theory, which is different from other books on SVMs in this respect. Optimization is one of the pillars on which SVMs are built, so it makes a lot of sense to consider them from this point of view''-- Read more...

✦ Table of Contents

Content: 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 epsilon-Band Hyperplane Linear Hard epsilon-Band Support Vector Regression Linear epsilon-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
Abstract: ''Preface Support vector machines (SVMs), which were introduced by Vapnik in the early 1990s, are proved effective and promising techniques for data mining. SVMs have recently been breakthroughs in advance in their theoretical studies and implementations of algorithms. They have been successfully applied in many fields such as text categorization, speech recognition, remote sensing image analysis, time series forecasting, information security and etc. SVMs, having their roots in Statistical Learning Theory (SLT) and optimization methods, become powerful tools to solve the problems of machine learning with finite training points and to overcome some traditional difficulties such as the ''curse of dimensionality'', ''over-fitting'' and etc. SVMs theoretical foundation and implementation techniques have been established and SVMs are gaining quick development and popularity due to their many attractive features: nice mathematical representations, geometrical explanations, good generalization abilities and promising empirical performance. Some SVM monographs, including more sophisticated ones such as Cristianini & Shawe-Taylor [39] and Scholkopf & Smola [124], have been published. We have published two books about SVMs in Science Press of China since 2004 [42, 43], which attracted widespread concerns and received favorable comments. After several years research and teaching, we decide to rewrite the books and add new research achievements. The starting point and focus of the book is optimization theory, which is different from other books on SVMs in this respect. Optimization is one of the pillars on which SVMs are built, so it makes a lot of sense to consider them from this point of view''