一对多分类
系统函数
随机抽取样本
randperm（n）
返回包含1：n随机排列的行向量
fmincg
使用非线性共轭梯度算法最小化函数，用法举例如下，
[theta] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)),initial_theta, options);
自定义函数
代价函数
lrCostFunction()
function [J, grad] = lrCostFunction(theta, X, y, lambda)
m = length(y);
J = 0;
grad = zeros(size(theta));
J = 1./m*(-y'*log(sigmoid(X*theta))-(1-y')*log(1-sigmoid(X*theta)));J = J + lambda/(2*m)*(sum(theta.^2)-theta(1).^2);grad = 1./m*X'*(sigmoid(X*theta)-y);grad = grad + lambda/m*theta;
grad(1) = grad(1) - lambda/m*theta(1);
grad = grad(:);end
定义梯度下降函数
function [all_theta] = oneVsAll(X, y, num_labels, lambda)
m = size(X, 1);
n = size(X, 2);
all_theta = zeros(num_labels, n + 1);
initial_theta = zeros(n+1,1);options = optimset('GradObj', 'on', 'MaxIter', 50);for c = 1:num_labels [theta] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)),initial_theta, options); all_theta(c,:) = theta';end
end
大的主要的流程是1、2、5、6
其中流程3是为了检验编写的函数是否能够达到目的，需要已有的数据结果进行对比
1、设置参数
input_layer_size = 400; % 20x20 Input Images of Digitsnum_labels = 10; % 10 labels, from 1 to 10
2、导入数据
load('ex3data1.mat'); % training data stored in arrays X, y
m = size(X, 1);
3、随机选组前100个例子进行展示
rand_indices = randperm(m);sel = X(rand_indices(1:100), :);
displayData(sel);
4、测试梯度下降函数（测试梯度下降函数）
% Test case for lrCostFunctionfprintf('\nTesting lrCostFunction() with regularization');theta_t = [-2; -1; 1; 2];X_t = [ones(5,1) reshape(1:15,5,3)/10];y_t = ([1;0;1;0;1] >= 0.5);lambda_t = 3;[J grad] = lrCostFunction(theta_t, X_t, y_t, lambda_t);
5、计算参数grad
lambda = 0.1;[all_theta] = oneVsAll(X, y, num_labels, lambda);
6、预测值与计算值对比，得出分类算法的准确率
pred = predictOneVsAll(all_theta, X);
fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
神经网络进行预测
系统函数
[c, p] = max(a3, [], 2);
[x, ix] = max ([1, 3, 5, 2, 5])
⇒ x = 5 ix = 3
定义函数
预测函数
function p = predict(Theta1, Theta2, X)
m = size(X, 1);
num_labels = size(Theta2, 1);
p = zeros(size(X, 1), 1);
X = [ones(m,1) X];
a2 = sigmoid(X*Theta1');
a2 = [ones(size(a2,1),1) a2];
a3 = (sigmoid(a2*Theta2'));
[c, p] = max(a3, [], 2);
1、设定参数
input_layer_size = 400; % 20x20 Input Images of Digitshidden_layer_size = 25; % 25 hidden unitsnum_labels = 10; % 10 labels, from 1 to 10
% (note that we have mapped "0" to label 10)
2、导入数据，显示部分随机的结果
fprintf('Loading and Visualizing Data ...\n')load('ex3data1.mat');m = size(X, 1);% Randomly select 100 data points to displaysel = randperm(size(X, 1));sel = sel(1:100);displayData(X(sel, :));
fprintf('Program paused. Press enter to continue.\n');
3、导入神经网络隐藏层参数Theta1和逻辑判断参数Theta2
% Load the weights into variables Theta1 and Theta2load('ex3weights.mat');
4、预测
pred = predict(Theta1, Theta2, X);fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
5、随机展示其中一个手写图像，输出预测结果
rp = randperm(m);
for i = 1:m % Display fprintf('\nDisplaying Example Image\n'); displayData(X(rp(i), :)); pred = predict(Theta1, Theta2, X(rp(i),:)); fprintf('\nNeural Network Prediction: %d (digit %d)\n', pred, mod(pred, 10)); % Pause with quit option s = input('Paused - press enter to continue, q to exit:','s'); if s == 'q' break endend
