1.简介

先给出资源地址：地址

该资源是我之前写的，matlab实现的简单的三层神经网络，自带了输入数据，可实现batchBP和singleBP，并可输出图像对比，所有函数都在这里没有任何附加函数，在这边分享一下，有不对的地方欢迎一起讨论~

2.代码

2.1主函数

输入数据为3类，共有30个样本

x = [1.58 2.32 -5.8;0.67 1.58 -4.78;1.04 1.01 -3.63;-1.49 2.18 -3.39;-0.41 1.21 -4.73;...
    1.39 3.16 2.87;1.2 1.4 -1.89;-0.92 1.44 -3.22;0.45 1.33 -4.38;-0.76 0.84 -1.96;...%第一类
    0.21 0.03 -2.21;0.37 0.28 -1.8;0.18 1.22 0.16;-0.24 0.93 -1.01;-1.18 0.39 -0.39;...
    0.74 0.96 -1.16;-0.38 1.94 -0.48;0.02 0.72 -0.17;0.44 1.31 -0.14;0.46 1.49 0.68;...%第二类
    -1.54 1.17 0.64;5.41 3.45 -1.33;1.55 0.99 2.69;1.86 3.19 1.51;1.68 1.79 -0.87;...
    3.51 -0.22 -1.39;1.4 -0.44 -0.92;0.44 0.83 1.97;0.25 0.68 -0.99;0.66 -0.45 0.08];%第三类
t = zeros(30,3);
t(1:10,1) = 1;
t(11:20,2) = 1;
t(21:30,3) = 1;

param.Nx = 30;
param.Nd = 3;
param.Ny = 3;

param.Nh = 6;%隐层节点个数
param.eta = 0.5;%权重更新率
param.theta = 1;%停止阈值

%初始化
Wh = 0.2*(rand(param.Nd,param.Nh)-0.5);
Wy = 0.2*(rand(param.Nh,param.Ny)-0.5);
w{1} = Wh;
w{2} = Wy;
[ J, z, yh ] = forward( x, w, t, param );

%批量方式更新权重
[ w1, count1, data1] = batchBP( x, z, yh, w, t, param );
%单样本方式更新权重
[ w2, count2, data2] = singleBP( x, z, yh, w, t, param );
%绘图
n1 = numel(find(data1 > 0));
data1 = data1(1:n1);
xx1 = 1:n1;
n2 = numel(find(data2 > 0));
data2 = data2(1:n2);
xx2 = 1:n2;
plot(xx1,data1,xx2,data2);
grid on
xlabel('迭代次数n')
ylabel('目标函数loss')
title('两种更新方法的loss随迭代次数的关系变化图') 
legend('批量方式更新权重','单样本方式更新权重')

2.2前向传播

function [ J, z, yh ] = forward( x, w, t, param )
%   x为输入样本， w为网络权重， t为输出真值，param为网络参数
%   x = Nx*Nd; Wh = Nd*Nh ; Wy = Nh*Ny; t = Nx*Ny
%   三层BP网络前向过程
%   J为能量损失， z为最后一层输出， yh为隐层输出
Nh = param.Nh;
Nx = param.Nx;
Nd = param.Nd;
Ny = param.Ny;

Wh = w{1};
Wy = w{2};

neth = x*Wh;
yh = tan_h(neth);

netj = yh*Wy;
z = sigmoid(netj);

J = zeros(Nx,1);
for k = 1:Nx
    J(k) = 0;
    for i = 1:Ny
        J(k) = (z(k,i) - t(k,i))^2 + J(k);
    end
end
J = 0.5*J;

end

2.3批量反传

function [ w, count, data] = batchBP( x, z, yh, w, t, param )
%BATCHBP 此处显示有关此函数的摘要
%   批量BP算法
Nh = param.Nh;
Nx = param.Nx;
Nd = param.Nd;
Ny = param.Ny;
eta = param.eta;
theta = param.theta;

flag = 0;
count = 0;
res = [0 0 0];
resid = 1;
m = 0;
data = zeros(30000,1);
q = 1;
while(flag == 0)
    Wh = w{1};
    Wy = w{2};
    sj = zeros(Nx,Ny);
    sh = zeros(Nx,Nh);
    deltaj = zeros(Nh,Ny);
    deltah = zeros(Nd,Nh);
    for k = 1:Nx
        for j = 1:Ny
            sj(k,j) = z(k,j)*(1-z(k,j))*(t(k,j)-z(k,j));
            for h = 1:Nh
                deltaj(h,j) = eta*sj(k,j)*yh(k,h) + deltaj(h,j);
            end
        end
        for h = 1:Nh
            sh(k,h) = (1-yh(k,h)^2)*(Wy(h,:)*sj(k,:)');
            for i = 1:Nd
                deltah(i,h) = eta*sh(k,h)*x(k,i) + deltah(i,h);
            end
        end
    end
    Wy = Wy + deltaj;
    Wh = Wh + deltah;
    w{1} = Wh;
    w{2} = Wy;
    [ J, z, yh ] = forward( x, w, t, param );
    JJ = sum(abs(J));
    data(q) = JJ;
    q = q + 1;
    [ out ] = test( w, x, t );
    res(resid) = JJ;
    resid = resid + 1;
    if resid == 4
        resid = 1;
    end
    if sum(abs(J)) < theta || isnan(JJ) || (round(res(1),3) == round(res(2),3) && round(res(1),3) == round(res(3),3))
        flag = 1;       
    end
    count = count + 1;
    disp(['batch迭代第' num2str(count) '次，正确率为：' num2str(out*100) '%, loss为：' num2str(JJ)]);

end
end

2.4单样本反传

function [ w, count, data] = singleBP( x, z, yh, w, t, param )
%BATCHBP 此处显示有关此函数的摘要
%   单样本更新BP算法
Nh = param.Nh;
Nx = param.Nx;
Nd = param.Nd;
Ny = param.Ny;
eta = param.eta;
theta = param.theta;

flag = 0;
count = 0;
res = [0 0 0];
resid = 1;
data = zeros(30000,1);
q = 1;
while(flag == 0)
    for k = 1:Nx
        Wh = w{1};
        Wy = w{2};
        sj = zeros(Nx,Ny);
        sh = zeros(Nx,Nh);
        deltaj = zeros(Nh,Ny);
        deltah = zeros(Nd,Nh);
        for j = 1:Ny
            sj(k,j) = z(k,j)*(1-z(k,j))*(t(k,j)-z(k,j));
            for h = 1:Nh
                deltaj(h,j) = eta*sj(k,j)*yh(k,h);
            end
        end
        for h = 1:Nh
            sh(k,h) = (1-yh(k,h)^2)*(Wy(h,:)*sj(k,:)');
            for i = 1:Nd
                deltah(i,h) = eta*sh(k,h)*x(k,i);
            end
        end
        Wy = Wy + deltaj;
        Wh = Wh + deltah;
        w{1} = Wh;
        w{2} = Wy;
        [ J, z, yh ] = forward( x, w, t, param );
        JJ = sum(abs(J));
        data(q) = JJ;
        q = q + 1;
        [ out ] = test( w, x, t );
        res(resid) = JJ;
        resid = resid + 1;
        if resid == 4
            resid = 1;
        end
        count = count + 1;
        disp(['single迭代第' num2str(count) '次，正确率为：' num2str(out*100) '%, loss为：' num2str(JJ)]);
        if sum(abs(J)) < theta || isnan(JJ) || (round(res(1),5) == round(res(2),5) && round(res(1),5) == round(res(3),5))
            flag = 1;
            break;
        end
    end
end
end

2.5测试函数

function [ out ] = test( w, x, t )
%TEST 此处显示有关此函数的摘要
%   此处显示详细说明
Wh = w{1};
Wy = w{2};

neth = x*Wh;
yh = tan_h(neth);

netj = yh*Wy;
z = sigmoid(netj);

[~,I] = max(z,[],2);
[~,It] = max(t,[],2);
tr = numel(find(I == It));
out = tr/size(x,1);

end

2.6激活函数

双曲正切函数

function [ y ] = tan_h( x )
%TAN_H 此处显示有关此函数的摘要
%   双曲正切函数
[a,b] = size(x);
y = zeros(a,b);
for i = 1:a
    for j = 1:b
        y(i,j) = (exp(x(i,j))-exp(-x(i,j)))/(exp(x(i,j))+exp(-x(i,j)));
    end
end
end

Sigmiod函数

function [ y ] = sigmoid( x )
%SIGMOID 此处显示有关此函数的摘要
%   此处显示详细说明
[a,b] = size(x);
y = zeros(a,b);
for i = 1:a
    for j = 1:b
        y(i,j) = 1/(1+exp(-x(i,j)));
    end
end
end

2.7输出结果

BP和SP的对比结果如下图