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Introduction to SVM

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.

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Introduction to SVM

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  1. Introduction to SVM Zhang Liliang

  2. 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

  3. 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”)

  4. Case 1: Linearly separable data; “Hard-margin” linear SVM Maximize the Gap!

  5. Statement of linear SVM classifier

  6. Statement of linear SVM classifier

  7. SVM optimization problem: Primal formulation Gap(Margin): Problem Transformation: max D -> min w -> min w^2 - > min 1/2(w^2)

  8. SVM optimization problem: Dual formulation

  9. Case 2: Not linearly separable data;“Soft-margin” linear SVM

  10. Parameter C in soft-margin SVM

  11. Not linearly separable data:

  12. Kernel trick

  13. Popular kernels

  14. Conclusion • SVM：Maximize the Gap(Margin) max D -> min w -> min w^2 - > min 1/2(w^2) Hard-margin: Soft-margin: Kernel trick:

  15. 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.pdf；（来自卡内基梅隆大学carnegie mellon university(CMU)的讲解SVM的PPT） • http://www.nyuinformatics.org/downloads/supplements/SVM_Tutorial_2010/Final_WB.pdf（A Gentle Introduction to Support Vector Machines in Biomedicine）

  16. Thanks~

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