三层神经网络反向传播算法matlab

以下是三层神经网络反向传播算法的 MATLAB 代码：

% 设置输入层、隐藏层和输出层的神经元个数
input_layer_size = 2;  % 输入层神经元个数
hidden_layer_size = 4; % 隐藏层神经元个数
num_labels = 1;        % 输出层神经元个数

% 初始化权重矩阵
Theta1 = rand(hidden_layer_size, input_layer_size + 1) * 2 - 1;  % 隐藏层权重矩阵
Theta2 = rand(num_labels, hidden_layer_size + 1) * 2 - 1;        % 输出层权重矩阵

% 加载训练数据
load('data.mat');

% 定义代价函数
function J = costFunction(X, y, Theta1, Theta2)
  % 前向传播计算输出值
  m = size(X, 1);
  a1 = [ones(m, 1) X];
  z2 = a1 * Theta1';
  a2 = [ones(m, 1) sigmoid(z2)];
  z3 = a2 * Theta2';
  h = sigmoid(z3);

  % 计算代价函数
  J = sum(-y .* log(h) - (1 - y) .* log(1 - h)) / m;
end

% 定义 sigmoid 函数
function g = sigmoid(z)
  g = 1 ./ (1 + exp(-z));
end

% 定义 sigmoid 函数的导数
function g = sigmoidGradient(z)
  g = sigmoid(z) .* (1 - sigmoid(z));
end

% 定义反向传播算法
function [Theta1_grad, Theta2_grad] = backpropagation(X, y, Theta1, Theta2)
  % 前向传播计算输出值
  m = size(X, 1);
  a1 = [ones(m, 1) X];
  z2 = a1 * Theta1';
  a2 = [ones(m, 1) sigmoid(z2)];
  z3 = a2 * Theta2';
  h = sigmoid(z3);

  % 计算误差
  delta3 = h - y;
  delta2 = delta3 * Theta2 .* sigmoidGradient([ones(m, 1) z2]);
  delta2 = delta2(:, 2:end);

  % 计算梯度
  Theta1_grad = delta2' * a1 / m;
  Theta2_grad = delta3' * a2 / m;
end

% 训练神经网络
options = optimset('MaxIter', 1000);
[nn_params, cost] = fmincg(@(p)(costFunction(X, y, reshape(p(1:hidden_layer_size * (input_layer_size + 1)), hidden_layer_size, input_layer_size + 1), reshape(p(hidden_layer_size * (input_layer_size + 1) + 1:end), num_labels, hidden_layer_size + 1))), [Theta1(:); Theta2(:)], options);
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), hidden_layer_size, input_layer_size + 1);
Theta2 = reshape(nn_params(hidden_layer_size * (input_layer_size + 1) + 1:end), num_labels, hidden_layer_size + 1);

% 预测新样本的输出值
x_new = [1.5, 2.0];  % 新样本的输入值
a1_new = [1 x_new];
z2_new = a1_new * Theta1';
a2_new = [1 sigmoid(z2_new)];
z3_new = a2_new * Theta2';
h_new = sigmoid(z3_new);

注：此代码是一个简单的三层神经网络的反向传播算法，只适用于二分类问题，如果要应用到多分类问题中，则需要做一些修改。