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Last active January 10, 2017 09:10
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機械学習を1ヵ月で実践レベルにする #11 (ニューラルネットワーク #1) ref: http://qiita.com/junichiro/items/7794cedf834a4f6ef52c
x =
\begin{bmatrix}
x_1 \\
x_2 \\
x_3
\end{bmatrix}
,
\theta =
\begin{bmatrix}
\theta_0 \\
\theta_1 \\
\theta_2 \\
\theta_3
\end{bmatrix}
x =
\begin{bmatrix}
x_0 \\
x_1 \\
x_2 \\
x_3
\end{bmatrix}
,
\theta =
\begin{bmatrix}
\theta_0 \\
\theta_1 \\
\theta_2 \\
\theta_3
\end{bmatrix}
,
x_0 = 1
h_\theta(x) = g(\theta^Tx)
g(z) = \frac{1}{1+e^{-z}}
a_1^{(2)} = g(\Theta_{10}^{(1)}x_0 + \Theta_{11}^{(1)}x_1 + \Theta_{12}^{(1)}x_2 + \Theta_{13}^{(1)}x_3) \\
a_2^{(2)} = g(\Theta_{20}^{(1)}x_0 + \Theta_{21}^{(1)}x_1 + \Theta_{22}^{(1)}x_2 + \Theta_{23}^{(1)}x_3) \\
a_3^{(2)} = g(\Theta_{30}^{(1)}x_0 + \Theta_{31}^{(1)}x_1 + \Theta_{32}^{(1)}x_2 + \Theta_{33}^{(1)}x_3) \\
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)})
\Theta^{(1)} =
\begin{bmatrix}
-30 & 10\\
20 & -20 \\
20 & -10
\end{bmatrix}
,
\Theta^{(2)} =
\begin{bmatrix}
-10 \\
20 \\
20
\end{bmatrix}
a_1^{(2)} = g(\Theta_{10}^{(1)}x_0 + \Theta_{11}^{(1)}x_1 + \Theta_{12}^{(1)}x_2) \\
a_2^{(2)} = g(\Theta_{20}^{(1)}x_0 + \Theta_{21}^{(1)}x_1 + \Theta_{22}^{(1)}x_2) \\
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)})
a_1^{(2)} = g(-30 + 20x_1 + 20x_2) \\
a_2^{(2)} = g(10 - 20x_1 - 10x_2) \\
h_\Theta(x) = a_1^{(3)} = g(-10 + \Theta_{11}^{(2)}a_1^{(2)} + \Theta_{12}^{(2)}a_2^{(2)})
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