@@ -407,10 +407,25 @@ from sklearn.linear_model import LogisticRegression
407407![ a_2^{(2)} = g(\theta _ {20}^{(1)}{x_0} + \theta _ {21}^{(1)}{x_1} + \theta _ {22}^{(1)}{x_2} + \theta _ {23}^{(1)}{x_3})] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=a_2%5E%7B%282%29%7D%20%3D%20g%28%5Ctheta%20_%7B20%7D%5E%7B%281%29%7D%7Bx_0%7D%20%2B%20%5Ctheta%20_%7B21%7D%5E%7B%281%29%7D%7Bx_1%7D%20%2B%20%5Ctheta%20_%7B22%7D%5E%7B%281%29%7D%7Bx_2%7D%20%2B%20%5Ctheta%20_%7B23%7D%5E%7B%281%29%7D%7Bx_3%7D%29 )
408408![ a_3^{(2)} = g(\theta _ {30}^{(1)}{x_0} + \theta _ {31}^{(1)}{x_1} + \theta _ {32}^{(1)}{x_2} + \theta _ {33}^{(1)}{x_3})] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=a_3%5E%7B%282%29%7D%20%3D%20g%28%5Ctheta%20_%7B30%7D%5E%7B%281%29%7D%7Bx_0%7D%20%2B%20%5Ctheta%20_%7B31%7D%5E%7B%281%29%7D%7Bx_1%7D%20%2B%20%5Ctheta%20_%7B32%7D%5E%7B%281%29%7D%7Bx_2%7D%20%2B%20%5Ctheta%20_%7B33%7D%5E%7B%281%29%7D%7Bx_3%7D%29 )
409409 - 输出层
410- ![ {h_ \theta }(x) = a_1^{(3)} = g(\theta _ {10}^{(2)}a_0^{(2)} + \theta _ {11}^{(2)}a_1^{(2)} + \theta _ {12}^{(2)}a_2^{(2)} + \theta _ {13}^{(2)}a_3^{(2)})] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bh_%5Ctheta%20%7D%28x%29%20%3D%20a_1%5E%7B%283%29%7D%20%3D%20g%28%5Ctheta%20_%7B10%7D%5E%7B%282%29%7Da_0%5E%7B%282%29%7D%20%2B%20%5Ctheta%20_%7B11%7D%5E%7B%282%29%7Da_1%5E%7B%282%29%7D%20%2B%20%5Ctheta%20_%7B12%7D%5E%7B%282%29%7Da_2%5E%7B%282%29%7D%20%2B%20%5Ctheta%20_%7B13%7D%5E%7B%282%29%7Da_3%5E%7B%282%29%7D%29 )
410+ ![ {h_ \theta }(x) = a_1^{(3)} = g(\theta _ {10}^{(2)}a_0^{(2)} + \theta _ {11}^{(2)}a_1^{(2)} + \theta _ {12}^{(2)}a_2^{(2)} + \theta _ {13}^{(2)}a_3^{(2)})] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bh_%5Ctheta%20%7D%28x%29%20%3D%20a_1%5E%7B%283%29%7D%20%3D%20g%28%5Ctheta%20_%7B10%7D%5E%7B%282%29%7Da_0%5E%7B%282%29%7D%20%2B%20%5Ctheta%20_%7B11%7D%5E%7B%282%29%7Da_1%5E%7B%282%29%7D%20%2B%20%5Ctheta%20_%7B12%7D%5E%7B%282%29%7Da_2%5E%7B%282%29%7D%20%2B%20%5Ctheta%20_%7B13%7D%5E%7B%282%29%7Da_3%5E%7B%282%29%7D%29 ) 其中， ** S型函数 ** ![ g(z) = \frac{1}{{1 + {e^{ - z}}}} ] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=g%28z%29%20%3D%20%5Cfrac%7B1%7D%7B%7B1%20%2B%20%7Be%5E%7B%20-%20z%7D%7D%7D%7D ) ，也成为 ** 激励函数 **
411411- 可以看出![ {\theta ^{(1)}}] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Ctheta%20%5E%7B%281%29%7D%7D ) 为3x4的矩阵，![ {\theta ^{(2)}}] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Ctheta%20%5E%7B%282%29%7D%7D ) 为1x4的矩阵
412412 - ![ {\theta ^{(j)}}] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%5Ctheta%20%5E%7B%28j%29%7D%7D ) ==》` j+1 ` 的单元数x（` j ` 层的单元数+1）
413413
414+ ### 2、代价函数
415+ - 假设最后输出的![ {h_ \Theta }(x) \in {R^K}] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7Bh_%5CTheta%20%7D%28x%29%20%5Cin%20%7BR%5EK%7D ) ，即代表输出层有K个单元
416+ - ![ J(\Theta ) = - \frac{1}{m}\sum\limits_ {i = 1}^m {\sum\limits_ {k = 1}^K {[ y_k^{(i)}\log {{({h_ \Theta }({x^{(i)}}))}_ k}} } + (1 - y_k^{(i)})\log {(1 - {h_ \Theta }({x^{(i)}}))_ k}]] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=J%28%5CTheta%20%29%20%3D%20%20-%20%5Cfrac%7B1%7D%7Bm%7D%5Csum%5Climits_%7Bi%20%3D%201%7D%5Em%20%7B%5Csum%5Climits_%7Bk%20%3D%201%7D%5EK%20%7B%5By_k%5E%7B%28i%29%7D%5Clog%20%7B%7B%28%7Bh_%5CTheta%20%7D%28%7Bx%5E%7B%28i%29%7D%7D%29%29%7D_k%7D%7D%20%7D%20%20%2B%20%281%20-%20y_k%5E%7B%28i%29%7D%29%5Clog%20%7B%281%20-%20%7Bh_%5CTheta%20%7D%28%7Bx%5E%7B%28i%29%7D%7D%29%29_k%7D%5D ) 其中，![ {({h_ \Theta }(x))_ i}] ( http://chart.apis.google.com/chart?cht=tx&chs=1x0&chf=bg,s,FFFFFF00&chco=000000&chl=%7B%28%7Bh_%5CTheta%20%7D%28x%29%29_i%7D ) 代表第` i ` 个单元输出
417+ - 与逻辑回归的代价函数差不多，就是累加上每个输出
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416431 [ 1 ] : ./images/LinearRegression_01.png " LinearRegression_01.png "
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