损失函数画图
- Hinge loss function：
\[H(z) = max(0,1-z)\]
- $\psi$-learning loss function:
\[{\phi _s}(z) = \left\{ {\begin{array}{*{20}{c}}
s&{z < 0}\\
0&{z \ge 0}
\end{array}} \right.\]
- Normalized Sigmoid loss:
\[{P_t}(z) = 1 - \tanh (tz)\]
- Ramp loss function:
\[{R_s}(z) = \left\{ {\begin{array}{*{20}{c}}
0&{z > 0}\\
{1 - z}&{0 \le z \le 1}\\
{1 - s}&{z > 1}
\end{array}} \right.\]
%plot loss function %define the loss function H = @(z)max(0,1-z) ; %Hinge loss function P = @(z)(2*(z<0)+0*(z>=0)); %\psi-learning loss function S = @(z)(1-tanh(2*z)); %Normalized Sigmoid loss function R = @(z)(1*(z<0)+(1-z).*(z>=0&z<1)+0*(z>=1)); % ramp loss z=-2:0.01:2; subplot(1,4,1) % plot the 1st figure of 1-4 plot(z,H(z),\'-\',\'linewidth\',2); xlabel(\'z\'); title(\'Hinge loss\',\'fontweight\',\'normal\',\'fontsize\',10); axis([-2,2 0 3]) subplot(1,4,2) plot(z,P(z),\'g-\',\'linewidth\',2); xlabel(\'z\'); title(\'\psi-learnig loss\',\'fontweight\',\'normal\',\'fontsize\',10); axis([-2,2 0 3]) subplot(1,4,3) plot(z,S(z),\'r-\',\'linewidth\',2); xlabel(\'z\'); title(\'Normalized Sigmoid loss\',\'fontweight\',\'normal\',\'fontsize\',10); axis([-2,2 0 3]) subplot(1,4,4) plot(z,R(z),\'b-\',\'linewidth\',2); xlabel(\'z\'); title(\'Ramp loss\',\'fontweight\',\'normal\',\'fontsize\',10); axis([-2,2 0 3])
