MATLAB 损失函数画图

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])