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

Language Support Version 5.3.36-SNAPSHOT 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

which use CMake ○ C++ modules support ● Working with the community to improve building software ○ ISO standards ■ Dependency format ○ Pushing forward modules support in other build systems ■ xmake needed to order compilations ● Vendored into CMake for its Unix Makefiles generator ● dyndep support added to ninja, merged into 1.10 (released Jan 2020) 11C++ Modules: Example Target add_library(A) up ○ Object (uniqueness constraint) ○ Source file ○ Work directory ○ Arguments (no “command” support) ● Additional fields ○ For modules build graph ■ Provides (mapping of module name to BMI path)

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

first high performance Nim - the first high performance language with full support for hot code- language with full support for hot code- reloading at runtime reloading at runtime by Viktor Kirilov backed by Mozilla (although with a lot less...) has a rich stdlib, package manager, docs, some IDE support 19 Feature rundown Feature rundown uniform call syntax (extension methods) - obj.method() OR method(obj) smaller scope for the compiler all the cutting-edge optimization for C/C++ for free out-of-the-box support for tons of platforms easiest C/C++ interop possible exceptions - reusing those of C++ when using

---------------- * fixed potential security risk when using Spring OXM with JAXB (SPR-10806) * support for Quartz 2.2 (SPR-10775) * updated spring-instrument manifest to include JDK 7 redefine/retransform (SPR-10567) Changes in version 3.2.2 (2013-03-14) ------------------------------------- * official support for Hibernate 4.2 (SPR-10255) * fixed missing inter-dependencies in module POMs (SPR-10218) * marked (SPR-10309) * fixed regression in SpringValidatorAdapter's retrieval of invalid values (SPR- 10243) * support 'unless' expression for cache veto (SPR-8871) * @Async's qualifier works for target class annotations

BlobStringType with configurable character encoding for both Hibernate2 and Hibernate3 * updated Spring's JDO support to be compatible with JPOX JDO 2.0 API snapshot-9 (corresponding to JDO 2.0 final draft) * JdoTransactionManager OrderForm, AccountForm and UserSession as Serializable Package org.springframework.scheduling * added support for Quartz 1.5's merged JobDataMap to QuartzJobBean, falling back to plain JobDataMap on Quartz ServletException (for nicer root cause handling) * "contextConfigLocation" params in "web.xml" support "${...}" style placeholders for system properties * deprecated BindUtils and BindInitializer in