神经网络原理和实现（MATLAB）

 

main.h

clear;
clc;
load mnist_uint8;

train_x = double(train_x')/255;
test_x = double(test_x')/255;
train_y = double(train_y');
test_y = double(test_y');
%每层的神经元数目，头和尾分别表示input和output
net = nnsetup([784 200 10]);

opts.alpha = 1;
opts.batchsize = 50;
opts.numepochs = 20;

net = nntrain(net, train_x, train_y, opts);
plot(net.rL);

err = nnpredict(net, test_x, test_y);
fprintf('err is %.2f\n', err*100);

nnsetup.m

% 初始化权值
function net = nnsetup(layers)
    net.size = layers;
    net.layers = numel(layers);
    net.inputs = layers(1);
    net.outputs = layers(net.layers);
    
    for i=1:net.layers-1
        net.layer{i}.w = (rand(layers(i+1), layers(i)+1)-0.5)/ layers(i);
    end
end

nnff.m

%前馈传导计算
function net = nnff(net, x)
    m = size(x, 2);
    net.layer{1}.a = x;
    
    for i=2:net.layers
        net.layer{i}.a = sigm(net.layer{i-1}.w * [net.layer{i-1}.a;ones(1, m)]);
    end
end

 

nnbp.m

%反向传导   
function net = nnbp(net, y)
    m = size(y, 2);
    
    net.e = net.layer{net.layers}.a-y;
    %  loss function
    net.L = 1/2* sum(net.e(:) .^ 2) / size(net.e, 2);
    
    %output layer
    net.layer{net.layers}.deta = net.e.* net.layer{net.layers}.a .*(1-net.layer{net.layers}.a);    
    %update
    net.layer{net.layers-1}.w = net.layer{net.layers-1}.w - net.layer{net.layers}.deta * [net.layer{net.layers-1}.a;ones(1, m)]' ./m;
    
    %hide layer 
    for k=net.layers-1:-1:2
        net.layer{k}.deta =net.layer{k}.w(:, 1:net.size(k))'*net.layer{k+1}.deta .* net.layer{k}.a.*(1-net.layer{k}.a);
        net.layer{k-1}.w = net.layer{k-1}.w - net.layer{k}.deta * [net.layer{k-1}.a; ones(1, m)]'./m; 
    end  
end    

nnpredict.m

function er =  nnpredict(net, test_x, test_y)
    net = nnff(net, test_x);
    o = net.layer{net.layers}.a;
    [~, h] = max(o);
    [~, a] = max(test_y);
    bad = find(h ~= a);

    er = numel(bad) / size(test_y, 2);
end