1.图片像素为20*20，X的属性数目为400，输出层神经元个数为10，分别代表1-10（把0映射为10）。
通过以下代码先形式化展示数据 ex3data1.mat内容：
load('ex3data1.mat'); % training data stored in arrays X, y m = size(X, 1); %求出样本总数 % Randomly select 100 data points to display rand_indices = randperm(m); %函数功能随机打乱这m个数字，输出给rand_indices. sel = X(rand_indices(1:100), :); %按照打乱后的数列取出100个数字，作为X矩阵的行数。 displayData(sel); %通过本函数将选出的X矩阵中100个样本进行图形化函数displayData()实现解析如下：
function [h, display_array] = displayData(X, example_width) %DISPLAYDATA Display 2D data in a nice grid if ~exist('example_width', 'var') || isempty(example_width) example_width = round(sqrt(size(X, 2))); %四舍五入求出图片的宽度 end colormap(gray); %将图片定义为灰色系 [m n] = size(X); example_height = (n / example_width); %求出图片的高度 % Compute number of items to display display_rows = floor(sqrt(m)); %计算出每行每列展示多少个数字图片 display_cols = ceil(m / display_rows); pad = 1; %图片之间间隔 % Setup blank display 创建要展示的图片像素大小，空像素，数字图片之间有1像素间隔 display_array = - ones(pad + display_rows * (example_height + pad), ... pad + display_cols * (example_width + pad)); % Copy each example into a patch on the display array 将像素点填充进去 curr_ex = 1; for j = 1:display_rows for i = 1:display_cols if curr_ex > m, break; end% Get the max value of the patch max_val = max(abs(X(curr_ex, :))); display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ... pad + (i - 1) * (example_width + pad) + (1:example_width)) = ... reshape(X(curr_ex, :), example_height, example_width) / max_val; %reshape函数进行矩阵维数转换 curr_ex = curr_ex + 1; end if curr_ex > m, break; end end h = imagesc(display_array, [-1 1]); %将像素点画为图片 axis image off %不显示坐标轴 drawnow; %刷新屏幕 end
2.向量化逻辑回归
向量化代价函数和梯度下降，代码同第三周编程练习相同：http://www.cnblogs.com/LoganGo/p/9009767.html
核心代码如下：
function [J, grad] = lrCostFunction(theta, X, y, lambda) m = length(y); % number of training examples J = 0; grad = zeros(size(theta));%分别计算代价值J和梯度grad J=1/m*(-(y')*log(sigmoid(X*theta))-(1-y)'*log(1-sigmoid(X*theta)))+lambda/(2*m)*(theta'*theta-theta(1)^2); %grad = 1/m*X'*(sigmoid(X*theta)-y)+lambda*theta/m; %grad(1) = grad(1)-lambda*theta(1)/m; grad=1/m*X'*(sigmoid(X*theta)-y)+lambda/m*([0;theta(2:end)]); grad = grad(:);end
3.逻辑回归解决多分类问题
oneVsAll.m函数解析：通过阅读原文中所给的英文解析，足够完成本函数的编写
function [all_theta] = oneVsAll(X, y, num_labels, lambda) m = size(X, 1); n = size(X, 2); all_theta = zeros(num_labels, n + 1); %为训练1-10个便签，所以需要矩阵为10*n+1 X = [ones(m, 1) X]; %运用了fmincg()函数求参数，与函数fminunc()相比，处理属性过多时更高效！ options = optimset('GradObj', 'on', 'MaxIter', 50); for c=1:num_labels, all_theta(c,:)=fmincg(@(t)(lrCostFunction(t, X, (y==c), lambda)), all_theta(c,:)', options)'; endend预测函数predictOneVsAll()函数编写：
function p = predictOneVsAll(all_theta, X) m = size(X, 1); num_labels = size(all_theta, 1); p = zeros(size(X, 1), 1); X = [ones(m, 1) X]; index=0; pre=zeros(num_labels,1); %存储每个样本对应数字1-10的预测值for c=1:m, for d=1:num_labels, pre(d)=sigmoid(X(c,:)*(all_theta(d,:)')); end [maxnum index]=max(pre); p(c)=index; %找到该样本最大的预测值所对应的数字，作为实际预测值 end end
二.神经网络解决多分类问题
使用已经训练好的参数θ1θ2来做预测，predict.m如下：
function p = predict(Theta1, Theta2, X) m = size(X, 1); num_labels = size(Theta2, 1); X=[ones(m,1) X]; %为a1添加为1的偏置 p = zeros(size(X, 1), 1); for i=1:m, %分别对m个样本做预测 a2=sigmoid(Theta1*X(i,:)'); %计算a2 a2=[1;a2]; %为a2添加为1的偏置 a3=sigmoid(Theta2*a2); %计算a3 [manum index]=max(a3); %求出哪个数字的预测值最大 p(i)=index; %得出预测值 end end
转载于:https://www.cnblogs.com/LoganGo/p/9057793.html
