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Support Vector Machine (Part 2) OUTLINE Multi-class classification Nonlinear mapping Kernel The Solution of Quiz-2 The maximum margin weight vector will be parallel to the shortest line connecting points of the two classes, that

  1. Support Vector Machine (Part 2)

  2. OUTLINE • Multi-class classification • Nonlinear mapping • Kernel

  3. The Solution of Quiz-2 • The maximum margin weight vector will be parallel to the shortest line connecting points of the two classes, that is, the line between (1,1) and (2,3), giving a weight vector of (1,2) • Working algebraically, with the standard constraint that: Minimize ||w|| subject to  • For some a; a+2a + b = -1 2a + 6a + b = 1 a= 2/5, b=- 11/5, so the optimal hyperplane is given by w = (2/5 , 4/5) and b = -11/5. 4 16 The large margin M is 2/ ||w||  2/ 25 + 25 = 5

  4. Multi-class Classification

  5. Multi-class Classification

  6. Multi-class Classification Source code example: http://scikit-learn.org/stable/modules/multiclass.html

  7. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  9. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  10. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  11. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  12. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  13. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  14. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  15. Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]

  17. Source: [http://sli.ics.uci.edu/Classes/2016W-178?action=download&upname=07_svm.pdf]

  21. Source: [https://class.coursera.org/ml-005/lecture/74]

  22. Source: [https://class.coursera.org/ml-005/lecture/74]

  23. Source: [https://class.coursera.org/ml-005/lecture/74]

  24. Source: [https://class.coursera.org/ml-005/lecture/74]

  25. Source: [https://class.coursera.org/ml-005/lecture/74]

  26. Gaussian Kernel Example (1) Source: [https://class.coursera.org/ml-005/lecture/74]

  27. Gaussian Kernel Example (2) Source: [https://class.coursera.org/ml-005/lecture/74]

  28. Gaussian Kernel Example (3) Source: [https://class.coursera.org/ml-005/lecture/74]

  29. Source: [https://class.coursera.org/ml-005/lecture/74]

  30. Source: [https://class.coursera.org/ml-005/lecture/74]

  31. Source: [https://class.coursera.org/ml-005/lecture/74]

  32. Source: [https://class.coursera.org/ml-005/lecture/74]

  33. Demo • http://scikit-learn.org/stable/modules/svm.html • http://scikit-learn.org/stable/auto_examples/plot_multilabel.html#example- plot-multilabel-py • http://scikit-learn.org/stable/auto_examples/svm/plot_svm_nonlinear.html • http://scikit-learn.org/stable/auto_examples/svm/plot_svm_kernels.html • http://scikit-learn.org/stable/auto_examples/svm/plot_custom_kernel.html

  34. References • http://cs229.stanford.edu/notes/cs229-notes3.pdf • https://class.coursera.org/ml-005/lecture/74 • http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf • http://nlp.stanford.edu/IR-book/html/htmledition/support-vector-machines-the- linearly-separable-case-1.html • http://www.holehouse.org/mlclass/12_Support_Vector_Machines.html

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