Transcript SVM-final

Introduction to SVM
Zhang Liliang
Outline
• SVM——SVM的概念和目的
• Hard Margin SVM——最原始的SVM及其
对偶形式
• Soft Margin SVM——引入松弛变量
• Kernel——解决低维到高维的映射
The Support Vector Machine (SVM)
approach
• The original Support vector machines (SVMs) is a binary
classification algorithm.
TARGET:Find out a linear decision surface (“hyperplane”)
Case 1: Linearly separable data;
“Hard-margin” linear SVM
Maximize the Gap!
Statement of linear SVM
classifier
Statement of linear SVM
classifier
SVM optimization problem:
Primal formulation
Gap(Margin):
Problem Transformation:
max D -> min w -> min w^2 - > min 1/2(w^2)
SVM optimization problem: Dual
formulation
Case 2: Not linearly separable
data;“Soft-margin” linear
SVM
Parameter C in soft-margin SVM
Not linearly separable data:
Kernel trick
Popular kernels
Conclusion
• SVM：Maximize the Gap(Margin)
max D -> min w -> min w^2 - > min 1/2(w^2)
Hard-margin:
Soft-margin:
Kernel trick:
Reference
• http://blog.csdn.net/v_july_v/article/details/
7624837（支持向量机通俗导论（理解
SVM的三层境界）by July）
• http://www.autonlab.org/tutorials/svm15.pd
f；（来自卡内基梅隆大学carnegie mellon
university(CMU)的讲解SVM的PPT）
• http://www.nyuinformatics.org/downloads/s
upplements/SVM_Tutorial_2010/Final_WB
.pdf（A Gentle Introduction to Support
Vector Machines in Biomedicine）
Thanks~