matlab练习程序（神经网络分类）

时间：2022-09-10 03:43:59

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：

matlab练习程序（神经网络分类）

分类结果：

matlab练习程序（神经网络分类）

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：

matlab练习程序（神经网络分类）

分类结果：

matlab练习程序（神经网络分类）

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：

matlab练习程序（神经网络分类）

分类结果：

matlab练习程序（神经网络分类）

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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