Lecture Notes on Support Vector Machine Feng Li fli@sdu.edu.cn Shandong University, China 1 Hyperplane and Margin In a n-dimensional space, a hyper plane is defined by ωT x + b = 0 (1) where ω ∈ Rn the margin is defined as γ = min i γ(i) (6) 1 ? ? ! ? ! Figure 1: Margin and hyperplane. 2 Support Vector Machine 2.1 Formulation The hyperplane actually serves as a decision boundary to differentiating samples are so-called support vector, i.e., the vectors “supporting” the margin boundaries. We can redefine ω by w = � s∈S αsy(s)x(s) where S denotes the set of the indices of the support vectors 4 Kernel

Lecture 6: Support Vector Machine Feng Li Shandong University fli@sdu.edu.cn December 28, 2021 Feng Li (SDU) SVM December 28, 2021 1 / 82 Outline 1 SVM: A Primal Form 2 Convex Optimization Review parallely along ω (b < 0 means in opposite direction) Feng Li (SDU) SVM December 28, 2021 3 / 82 Support Vector Machine A hyperplane based linear classifier defined by ω and b Prediction rule: y = sign(ωTx Scaling ! and " such that min& ' & !() & + " = 1 Feng Li (SDU) SVM December 28, 2021 14 / 82 Support Vector Machine (Primal Form) Maximizing 1/∥ω∥ is equivalent to minimizing ∥ω∥2 = ωTω min ω,b ωTω

1 Shiro support for the Spring Security plugin Table of contents 2 Shiro support for the Spring Security plugin - Reference Documentation Authors: Burt Beckwith Version: 0.1 Table of Contents 1 History 2 Usage 3 Configuration 3 1 Introduction The Spring Security Shiro plugin adds some support for using a hybrid approach combining Spring Security and . It currently only supports Shiro ACLs

1 Shiro support for the Spring Security plugin Shiro support for the Spring Security plugin - Reference Documentation Authors: Burt Beckwith Version: 1.0.0 Table of Contents 1 Introduction to the 1 Introduction to the Spring Security Shiro Plugin The Spring Security Shiro plugin adds some support for using a hybrid approach combining Spring and . It currently only supports Shiro ACLs, since

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Language Support Version 6.0.0-M2 Table of Contents 1. Kotlin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3. Dynamic Language Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . interoperability with existing libraries written in Java. The Spring Framework provides first-class support for Kotlin and lets developers write Kotlin applications almost as if the Spring Framework was a

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