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])
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