損失函數畫圖

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])

總結

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