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

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Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . 102 7 Remote virtual machines 103 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.1.1 Common third-party RDP viewers

Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . 102 7 Remote virtual machines 103 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.1.1 Common third-party RDP viewers

Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . 101 7 Remote virtual machines 102 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7.1.1 Common third-party RDP viewers

Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . 102 7 Remote virtual machines 103 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.1.1 Common third-party RDP viewers

Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . . 98 7 Remote virtual machines 99 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.1.1 Common third-party RDP viewers

Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . . 98 7 Remote virtual machines 99 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.1.1 Common third-party RDP viewers

Serial ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.10 USB support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.10.1 USB settings Limiting bandwidth for disk images . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.9 CD/DVD support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.10 iSCSI servers . . . . . . . . . . . . . . . . . . . . 94 7 Remote virtual machines 95 7.1 Remote display (VRDP support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.1.1 Common third-party RDP viewers