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

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 1.16 Python 3 Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 1.17 working as they should. Too much customizability would break this promise. Click was written to support the Flask microframework ecosystem because no tool could provide it with the function- ality it needed This goes against Click’s ambitions of dispatching to subparsers. • argparse currently does not support disabling of interspersed arguments. Without this feature it’s not possible to safely implement Click’s

prefer it to documentation. It basically can’t be wrong.” “What other framework has integrated support for ‘786 TRY IT NOW’ ?” Features Falcon tries to do as little as possible while remaining highly of URIs to resources Global, resource, and method hooks Idiomatic HTTP error responses Full Unicode support Intuitive request and response objects Works great with async libraries like gevent Minimal attack fact, Falcon only has two dependencies: six [http://pythonhosted.org/six/], to make it easier to support both Python 2 and 3, and mimeparse [https://code.google.com/p/mimeparse/] for handling complex Accept