matlab练习程序（神经网络识别mnist手写数据集）
mnist数据集训练数据一共有28*28*60000个像素，标签有60000个。
测试数据一共有28*28*10000个，标签10000个。
这里神经网络输入层是784个像素，用了100个隐含层，最终10个输出结果。
arc代表的是神经网络结构，可以增加隐含层，不过我试了没太大效果，毕竟梯度消失。
因为是最普通的神经网络，最终识别错误率大概在5%左右。
迭代曲线：
代码如下：
clear all;
close all;
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);
mu=mean(train_x);
sigma=max(std(train_x),eps);
train_x=bsxfun(@minus,train_x,mu); %每个样本分别减去平均值
train_x=bsxfun(@rdivide,train_x,sigma); %分别除以标准差
test_x=bsxfun(@minus,test_x,mu);
test_x=bsxfun(@rdivide,test_x,sigma);
arc = ; %输入784，隐含层100,输出10
n=numel(arc);
W = cell(1,n-1); %权重矩阵
for i=2:n
W{i-1} = (rand(arc(i),arc(i-1)+1)-0.5) * 8 *sqrt(6 / (arc(i)+arc(i-1)));
end
learningRate = 2; %训练速度
numepochs = 5; %训练5遍
batchsize = 100; %一次训练100个数据
m = size(train_x, 1); %数据总量
numbatches = m / batchsize; %一共有numbatches这么多组
%% 训练
L = zeros(numepochs*numbatches,1);
ll=1;
for i = 1 :
numepochs
kk = randperm(m);
for l = 1 :
numbatches
batch_x = train_x(kk((l - 1) * batchsize + 1 : l * batchsize), :);
batch_y = train_y(kk((l - 1) * batchsize + 1 : l * batchsize), :);
%% 正向传播
mm = size(batch_x,1);
x = ;
a{1} = x;
for ii = 2 : n-1
a{ii} = 1.7159*tanh(2/3.*(a{ii - 1} * W{ii - 1}'));
a{ii} = ;
end
a{n} = 1./(1+exp(-(a{n - 1} * W{n - 1}')));
e = batch_y - a{n};
L(ll) = 1/2 * sum(sum(e.^2)) / mm;
ll=ll+1;
%% 反向传播
d{n} = -e.*(a{n}.*(1 - a{n}));
for ii = (n - 1) : -1 : 2
d_act = 1.7159 * 2/3 * (1 - 1/(1.7159)^2 * a{ii}.^2);
if ii+1==n
d{ii} = (d{ii + 1} * W{ii}) .* d_act;
else
d{ii} = (d{ii + 1}(:,2:end) * W{ii}).* d_act; end
end
for ii = 1 : n-1
if ii + 1 == n
dW{ii} = (d{ii + 1}' * a{ii}) / size(d{ii + 1}, 1);
else
dW{ii} = (d{ii + 1}(:,2:end)' * a{ii}) / size(d{ii + 1}, 1);
end
end
%% 更新参数
for ii = 1 : n - 1
W{ii} = W{ii} - learningRate*dW{ii};
end
end
end
%% 测试，相当于把正向传播再走一遍
mm = size(test_x,1);
x = ;
a{1} = x;
for ii = 2 : n-1
a{ii} = 1.7159 * tanh( 2/3 .* (a{ii - 1} * W{ii - 1}'));
a{ii} = ;
end
a{n} = 1./(1+exp(-(a{n - 1} * W{n - 1}')));
[~, i] = max(a{end},[],2);
labels = i; %识别后打的标签
[~, expected] = max(test_y,[],2);
bad = find(labels ~= expected); %有哪些识别错了
er = numel(bad) / size(x, 1)； %错误率
plot(L);
测试数据：
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