matlab练习程序（神经网络分类）
注：这里的练习鉴于当时理解不完全，可能会有些错误，关于神经网络的实践可以参考我的这篇博文
这里的代码只是简单的练习，不涉及代码优化，也不涉及神经网络优化，所以我用了最能体现原理的方式来写的代码。
激活函数用的是h = 1/(1+exp(-y))，其中y=sum([X Y].*w)。
代价函数用的是E = 1/2*(t-h)^2，其中t为目标值，t为1代表是该类，t为0代表不是该类。
权值更新采用BP算法。
网络1形式如下，没有隐含层，1个偏置量，输入直接连接输出：
分类结果：
代码如下：
clear all;
close all;
clc; n=;
randn('seed',);
mu1=[ ];
S1=[0.5 ;
0.5];
P1=mvnrnd(mu1,S1,n); mu2=[ ];
S2=[0.5 ;
0.5];
P2=mvnrnd(mu2,S2,n); mu3=[ ];
S3=[0.5 ;
0.5];
P3=mvnrnd(mu3,S3,n); P=[P1;P2;P3];
meanP=mean(P); P=[P(:,)-meanP() P(:,)-meanP()]; sigma = ; X=P(:,);
Y=P(:,);
B=rand(*n,); w1 = rand(*n,);
w2 = rand(*n,);
w3 = rand(*n,); w4 = rand(*n,);
w5 = rand(*n,);
w6 = rand(*n,); for i=:*n
i
while y1 = X(i)*w1(i) + Y(i)*w4(i) + B(i);
y2 = X(i)*w2(i) + Y(i)*w5(i) + B(i);
y3 = X(i)*w3(i) + Y(i)*w6(i) + B(i); h1 = /(+exp(-y1));
h2 = /(+exp(-y2));
h3 = /(+exp(-y3)); e1 = /*( - h1)^;
e2 = /*( - h2)^;
e3 = /*( - h3)^; if i<=n && e1<=0.0000001
break;
elseif i>n && i<=*n && e2<0.0000001
break;
elseif i>*n && e3<0.0000001
break;
end if i<=n
w1(i) = w1(i)-sigma*(h1-)*h1*(-h1)*X(i);
w2(i) = w2(i)-sigma*(h2-)*h2*(-h2)*X(i);
w3(i) = w3(i)-sigma*(h3-)*h3*(-h3)*X(i); w4(i) = w4(i)-sigma*(h1-)*h1*(-h1)*Y(i);
w5(i) = w5(i)-sigma*(h2-)*h2*(-h2)*Y(i);
w6(i) = w6(i)-sigma*(h3-)*h3*(-h3)*Y(i); B(i) =B(i)- sigma*((h1-)*h1*(-h1)+(h2-)*h2*(-h2)+(h3-)*h3*(-h3));
elseif i>n && i<=*n
w1(i) = w1(i)-sigma*(h1-)*h1*(-h1)*X(i);
w2(i) = w2(i)-sigma*(h2-)*h2*(-h2)*X(i);
w3(i) = w3(i)-sigma*(h3-)*h3*(-h3)*X(i); w4(i) = w4(i)-sigma*(h1-)*h1*(-h1)*Y(i);
w5(i) = w5(i)-sigma*(h2-)*h2*(-h2)*Y(i);
w6(i) = w6(i)-sigma*(h3-)*h3*(-h3)*Y(i); B(i) =B(i)- sigma*((h1-)*h1*(-h1)+(h2-)*h2*(-h2)+(h3-)*h3*(-h3));
else
w1(i) = w1(i)-sigma*(h1-)*h1*(-h1)*X(i);
w2(i) = w2(i)-sigma*(h2-)*h2*(-h2)*X(i);
w3(i) = w3(i)-sigma*(h3-)*h3*(-h3)*X(i); w4(i) = w4(i)-sigma*(h1-)*h1*(-h1)*Y(i);
w5(i) = w5(i)-sigma*(h2-)*h2*(-h2)*Y(i);
w6(i) = w6(i)-sigma*(h3-)*h3*(-h3)*Y(i); B(i) =B(i)- sigma*((h1-)*h1*(-h1)+(h2-)*h2*(-h2)+(h3-)*h3*(-h3));
end end
end plot(P(:,),P(:,),'o');
hold on; flag = ;
M=[];
for x=-:0.3:
for y=-:0.3: H=[];
for i=:*n
y1 = x*w1(i)+y*w4(i) +B(i);
y2 = x*w2(i)+y*w5(i) +B(i);
y3 = x*w3(i)+y*w6(i) +B(i);
h1=/(+exp(-y1));
h2=/(+exp(-y2));
h3=/(+exp(-y3)); H=[H;h1 h2 h3];
end
% H1 = mean(H(:n,));
% H2 = mean(H(n:*n,));
% H3 = mean(H(*n:*n,)); meanH = mean(H);
H1 = meanH();
H2 = meanH();
H3= meanH();
if H1>H2 && H1>H3
plot(x,y,'g.')
elseif H2 > H1 && H2 > H3
plot(x,y,'r.')
elseif H3 > H1 && H3 > H2
plot(x,y,'b.')
end end
end
网络2形式如下，有1个隐含层，2个偏置量：
分类结果：
代码如下：
clear all;
close all;
clc; n=;
randn('seed',);
mu1=[ ];
S1=[0.5 ;
0.5];
P1=mvnrnd(mu1,S1,n); mu2=[ ];
S2=[0.5 ;
0.5];
P2=mvnrnd(mu2,S2,n); mu3=[ ];
S3=[0.5 ;
0.5];
P3=mvnrnd(mu3,S3,n); P=[P1;P2;P3];
meanP=mean(P); P=[P(:,)-meanP() P(:,)-meanP()]; sigma = ; X=P(:,);
Y=P(:,); B1=rand(*n,);
B2=rand(*n,); w1 = rand(*n,);
w2 = rand(*n,); w3 = rand(*n,);
w4 = rand(*n,);
w5 = rand(*n,); for i=:*n
i
while y0 = X(i)*w1(i) + Y(i)*w2(i) + B1(i);
h0 = /(+exp(-y0)); y1 = h0*w3(i) + B2(i);
y2 = h0*w4(i) + B2(i);
y3 = h0*w5(i) + B2(i); h1 = /(+exp(-y1));
h2 = /(+exp(-y2));
h3 = /(+exp(-y3)); e1 = /*( - h1)^;
e2 = /*( - h2)^;
e3 = /*( - h3)^; if i<=n && e1<=0.0000001
break;
elseif i>n && i<=*n && e2<0.0000001
break;
elseif i>*n && e3<0.0000001
break;
end %e1
if i<=n w1(i) = w1(i)- sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0)*X(i) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0)*X(i) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)*X(i));
w2(i) = w2(i)- sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0)*Y(i) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0)*Y(i) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)*Y(i));
B1(i) = B1(i)- sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)); w3(i) = w3(i)-sigma*(h1-)*h1*(-h1)*h0;
w4(i) = w4(i)-sigma*(h2-)*h2*(-h2)*h0;
w5(i) = w5(i)-sigma*(h3-)*h3*(-h3)*h0;
B2(i) =B2(i)- sigma*((h1-)*h1*(-h1)+(h2-)*h2*(-h2)+(h3-)*h3*(-h3)); elseif i>n && i<=*n
w1(i) = w1(i)-sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0)*X(i) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0)*X(i) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)*X(i));
w2(i) = w2(i)-sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0)*Y(i) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0)*Y(i) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)*Y(i));
B1(i) =B1(i)- sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)); w3(i) = w3(i)-sigma*(h1-)*h1*(-h1)*h0;
w4(i) = w4(i)-sigma*(h2-)*h2*(-h2)*h0;
w5(i) = w5(i)-sigma*(h3-)*h3*(-h3)*h0;
B2(i) =B2(i)- sigma*((h1-)*h1*(-h1)+(h2-)*h2*(-h2)+(h3-)*h3*(-h3)); else
w1(i) = w1(i)-sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0)*X(i) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0)*X(i) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)*X(i));
w2(i) = w2(i)-sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0)*Y(i) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0)*Y(i) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)*Y(i));
B1(i) =B1(i)- sigma*((h1-)*h1*(-h1)*w3(i)*h0*(-h0) + (h2-)*h2*(-h2)*w4(i)*h0*(-h0) + (h3-)*h3*(-h3)*w5(i)*h0*(-h0)); w3(i) = w3(i)-sigma*(h1-)*h1*(-h1)*h0;
w4(i) = w4(i)-sigma*(h2-)*h2*(-h2)*h0;
w5(i) = w5(i)-sigma*(h3-)*h3*(-h3)*h0;
B2(i) =B2(i)- sigma*((h1-)*h1*(-h1)+(h2-)*h2*(-h2)+(h3-)*h3*(-h3)); end end
end plot(P(:,),P(:,),'o');
hold on; flag = ;
M=[];
for x=-:0.3:
for y=-:0.3: H=[];
for i=:*n
y0 = x*w1(i)+y*w2(i) +B1(i);
h0=/(+exp(-y0)); y1 = h0*w3(i) + B2(i);
y2 = h0*w4(i) + B2(i);
y3 = h0*w5(i) + B2(i); h1 =/(+exp(-y1));
h2 =/(+exp(-y2));
h3 =/(+exp(-y3)); H=[H;h1 h2 h3];
end meanH = mean(H);
H1 = meanH();
H2 = meanH();
H3= meanH();
if H1>H2 && H1>H3
plot(x,y,'g.')
elseif H2 > H1 && H2 > H3
plot(x,y,'r.')
elseif H3 > H1 && H3 > H2
plot(x,y,'b.')
end end
end
网络3形式如下，有2个隐含层，2个偏置量：
分类结果：
代码如下：
clear all;
close all;
clc; n=;
randn('seed',);
mu1=[ ];
S1=[0.5 ;
0.5];
P1=mvnrnd(mu1,S1,n); mu2=[ ];
S2=[0.5 ;
0.5];
P2=mvnrnd(mu2,S2,n); mu3=[ ];
S3=[0.5 ;
0.5];
P3=mvnrnd(mu3,S3,n); P=[P1;P2;P3];
meanP=mean(P); P=[P(:,)-meanP() P(:,)-meanP()]; sigma = ; X=P(:,);
Y=P(:,); B1=rand(*n,);
B2=rand(*n,); w1 = rand(*n,);
w2 = rand(*n,); w3 = rand(*n,);
w4 = rand(*n,); w5 = rand(*n,);
w6 = rand(*n,);
w7 = rand(*n,); w8 = rand(*n,);
w9 = rand(*n,);
w10 = rand(*n,); for i=:*n
i
while y1 = X(i)*w1(i) + Y(i)*w3(i) + B1(i);
y2 = X(i)*w2(i) + Y(i)*w4(i) + B1(i); h1 = /(+exp(-y1));
h2 = /(+exp(-y2)); dh1 = h1*(-h1);
dh2 = h2*(-h2); y3 = h1*w5(i) + h2*w8(i)+ B2(i);
y4 = h1*w6(i) + h2*w9(i)+ B2(i);
y5 = h1*w7(i) + h2*w10(i)+ B2(i); h3 = /(+exp(-y3));
h4 = /(+exp(-y4));
h5 = /(+exp(-y5)); dh3 = h3*(-h3);
dh4 = h4*(-h4);
dh5 = h5*(-h5); e1 = /*( - h3)^;
e2 = /*( - h4)^;
e3 = /*( - h5)^; if i<=n && e1<=0.0000001
break;
elseif i>n && i<=*n && e2<0.0000001
break;
elseif i>*n && e3<0.0000001
break;
end %e1
if i<=n w1(i) = w1(i) -sigma * ((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i)) * dh1*X(i);
w2(i) = w2(i) -sigma * ((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i)) * dh2*X(i); w3(i) = w3(i) -sigma * ((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i)) * dh1*Y(i);
w4(i) = w4(i) -sigma * ((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i)) * dh2*Y(i); B1(i) = B1(i)- sigma*(((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i))*dh1+((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i))*dh2); w5(i) = w5(i)-sigma*(h3-)*dh3*h1;
w6(i) = w6(i)-sigma*(h4-)*dh4*h1;
w7(i) = w7(i)-sigma*(h5-)*dh5*h1; w8(i) = w8(i)-sigma*(h3-)*dh3*h2;
w9(i) = w9(i)-sigma*(h4-)*dh4*h2;
w10(i) = w10(i)-sigma*(h5-)*dh5*h2; B2(i) =B2(i)- sigma*((h3-)*dh3+(h4-)*dh4+(h5-)*dh5); elseif i>n && i<=*n
w1(i) = w1(i) -sigma * ((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i)) * dh1*X(i);
w2(i) = w2(i) -sigma * ((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i)) * dh2*X(i); w3(i) = w3(i) -sigma * ((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i)) * dh1*Y(i);
w4(i) = w4(i) -sigma * ((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i)) * dh2*Y(i); B1(i) = B1(i)- sigma*(((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i))*dh1+((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i))*dh2); w5(i) = w5(i)-sigma*(h3-)*dh3*h1;
w6(i) = w6(i)-sigma*(h4-)*dh4*h1;
w7(i) = w7(i)-sigma*(h5-)*dh5*h1; w8(i) = w8(i)-sigma*(h3-)*dh3*h2;
w9(i) = w9(i)-sigma*(h4-)*dh4*h2;
w10(i) = w10(i)-sigma*(h5-)*dh5*h2; B2(i) =B2(i)- sigma*((h3-)*dh3+(h4-)*dh4+(h5-)*dh5); else
w1(i) = w1(i) -sigma * ((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i)) * dh1*X(i);
w2(i) = w2(i) -sigma * ((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i)) * dh2*X(i); w3(i) = w3(i) -sigma * ((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i)) * dh1*Y(i);
w4(i) = w4(i) -sigma * ((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i)) * dh2*Y(i); B1(i) = B1(i)- sigma*(((h3-)*dh3*w5(i)+(h4-)*dh4*w6(i)+(h5-)*dh5*w7(i))*dh1+((h3-)*dh3*w8(i)+(h4-)*dh4*w9(i)+(h5-)*dh5*w10(i))*dh2); w5(i) = w5(i)-sigma*(h3-)*dh3*h1;
w6(i) = w6(i)-sigma*(h4-)*dh4*h1;
w7(i) = w7(i)-sigma*(h5-)*dh5*h1; w8(i) = w8(i)-sigma*(h3-)*dh3*h2;
w9(i) = w9(i)-sigma*(h4-)*dh4*h2;
w10(i) = w10(i)-sigma*(h5-)*dh5*h2; B2(i) =B2(i)- sigma*((h3-)*dh3+(h4-)*dh4+(h5-)*dh5); end end
end plot(P(:,),P(:,),'o');
hold on; flag = ;
M=[];
for x=-:0.3:
for y=-:0.3:
% x=-;
% y=;
H=[];
for i=:*n
y1 = x*w1(i) + y*w3(i) + B1(i);
y2 = x*w2(i) + y*w4(i) + B1(i); h1 = /(+exp(-y1));
h2 = /(+exp(-y2)); dh1 = h1*(-h1);
dh2 = h2*(-h2); y3 = h1*w5(i) + h2*w8(i)+ B2(i);
y4 = h1*w6(i) + h2*w9(i)+ B2(i);
y5 = h1*w7(i) + h2*w10(i)+ B2(i); h3 = /(+exp(-y3));
h4 = /(+exp(-y4));
h5 = /(+exp(-y5)); H=[H;h3 h4 h5];
end
% H1 = mean(H(:n,));
% H2 = mean(H(n+:*n,));
% H3 = mean(H(*n+:*n,)); meanH = mean(H);
H1 = meanH();
H2 = meanH();
H3= meanH(); M=[M;H1 H2 H3 x y];
if H1>H2 && H1>H3
plot(x,y,'g.')
elseif H2 > H1 && H2 > H3
plot(x,y,'r.')
elseif H3 > H1 && H3 > H2
plot(x,y,'b.')
end end
end
后面我计划对网络分别使用softmax，权重初始化，正则化，ReLu激活函数，交叉熵代价函数与卷积的形式进行优化。
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