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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 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.
The large margin M is 2/ ||w|| 2/4
25+
16
25= 5
Multi-class Classification
Multi-class Classification
Multi-class Classification
Source code example: http://scikit-learn.org/stable/modules/multiclass.html
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://www.cs.stevens.edu/~mordohai/classes/cs559_s10/Week10.pdf]
Source: [http://sli.ics.uci.edu/Classes/2016W-178?action=download&upname=07_svm.pdf]
Gaussian Kernel Example (1)
Source: [https://class.coursera.org/ml-005/lecture/74]
Gaussian Kernel Example (2)
Source: [https://class.coursera.org/ml-005/lecture/74]
Gaussian Kernel Example (3)
Source: [https://class.coursera.org/ml-005/lecture/74]
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
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
