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SVM
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@@ -672,9 +672,8 @@ def predict(Theta1,Theta2,X):
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![\left\{ {\begin{array}{c} {{\theta ^T}{x^{(i)}} \geqslant 1} \\ {{\theta ^T}{x^{(i)}} \leqslant - 1} \end{array} } \right.\begin{array}{c} {({y^{(i)}} = 1)} \\ {({y^{(i)}} = 0)} \end{array} ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cleft%5C%7B%20%7B%5Cbegin%7Barray%7D%7Bc%7D%20%20%20%20%7B%7B%5Ctheta%20%5ET%7D%7Bx%5E%7B%28i%29%7D%7D%20%5Cgeqslant%201%7D%20%5C%5C%20%20%20%20%7B%7B%5Ctheta%20%5ET%7D%7Bx%5E%7B%28i%29%7D%7D%20%5Cleqslant%20%20-%201%7D%20%20%5Cend%7Barray%7D%20%7D%20%5Cright.%5Cbegin%7Barray%7D%7Bc%7D%20%20%20%20%7B%28%7By%5E%7B%28i%29%7D%7D%20%3D%201%29%7D%20%5C%5C%20%20%20%20%7B%28%7By%5E%7B%28i%29%7D%7D%20%3D%200%29%7D%20%20%5Cend%7Barray%7D%20)可以得到:
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![\left\{ {\begin{array}{c} {{p^{(i)}}||\theta || \geqslant 1} \\ {{p^{(i)}}||\theta || \leqslant - 1} \end{array} } \right.\begin{array}{c} {({y^{(i)}} = 1)} \\ {({y^{(i)}} = 0)} \end{array} ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cleft%5C%7B%20%7B%5Cbegin%7Barray%7D%7Bc%7D%20%20%20%20%7B%7Bp%5E%7B%28i%29%7D%7D%7C%7C%5Ctheta%20%7C%7C%20%5Cgeqslant%201%7D%20%5C%5C%20%20%20%20%7B%7Bp%5E%7B%28i%29%7D%7D%7C%7C%5Ctheta%20%7C%7C%20%5Cleqslant%20%20-%201%7D%20%20%5Cend%7Barray%7D%20%7D%20%5Cright.%5Cbegin%7Barray%7D%7Bc%7D%20%20%20%20%7B%28%7By%5E%7B%28i%29%7D%7D%20%3D%201%29%7D%20%5C%5C%20%20%20%20%7B%28%7By%5E%7B%28i%29%7D%7D%20%3D%200%29%7D%20%20%5Cend%7Barray%7D%20)`p`即为`x``θ`上的投影
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- 如下图所示,假设决策边界如图,找其中的一个点,到`θ`上的投影为`p`,则![p||\theta || \geqslant 1](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=p%7C%7C%5Ctheta%20%7C%7C%20%5Cgeqslant%201)或者![p||\theta || \leqslant - 1](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=p%7C%7C%5Ctheta%20%7C%7C%20%5Cleqslant%20%20-%201),若是`p`很小,则需要![||\theta ||](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7C%7C%5Ctheta%20%7C%7C)很大,这与我们要求的`θ`使![||\theta || = \frac{1}{2}\sqrt {\theta _1^2 + \theta _2^2} ](http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7C%7C%5Ctheta%20%7C%7C%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Csqrt%20%7B%5Ctheta%20_1%5E2%20%2B%20%5Ctheta%20_2%5E2%7D%20)最小相违背,**所以**最后求的是`large margin`
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![enter description here][28]
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[1]: ./images/LinearRegression_01.png "LinearRegression_01.png"
@@ -703,4 +702,5 @@ def predict(Theta1,Theta2,X):
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[24]: ./images/SVM_01.png "SVM_01.png"
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[25]: ./images/SVM_02.png "SVM_02.png"
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[26]: ./images/SVM_03.png "SVM_03.png"
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[27]: ./images/SVM_04.png "SVM_04.png"
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[27]: ./images/SVM_04.png "SVM_04.png"
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[28]: ./images/SVM_05.png "SVM_05.png"

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