多层感知器神经网络模型matlab代码

以下是一个简单的多层感知器神经网络模型的 Matlab 代码示例。该模型包含一个输入层、一个隐藏层和一个输出层。

% 设置训练数据
input_data = [0 0; 0 1; 1 0; 1 1];
output_data = [0; 1; 1; 0];

% 初始化参数
hidden_layer_size = 4;
input_layer_size = size(input_data, 2);
output_layer_size = size(output_data, 2);
learning_rate = 0.1;
num_iterations = 10000;

% 随机初始化权重和偏置
theta1 = rand(hidden_layer_size, input_layer_size + 1);
theta2 = rand(output_layer_size, hidden_layer_size + 1);

% 训练模型
for i = 1:num_iterations
    % 前向传播
    input_data_with_bias = [ones(size(input_data, 1), 1) input_data];
    hidden_layer_input = input_data_with_bias * theta1';
    hidden_layer_output = sigmoid(hidden_layer_input);
    hidden_layer_output_with_bias = [ones(size(hidden_layer_output, 1), 1) hidden_layer_output];
    output_layer_input = hidden_layer_output_with_bias * theta2';
    output_layer_output = sigmoid(output_layer_input);

    % 反向传播
    output_layer_error = output_layer_output - output_data;
    hidden_layer_error = (output_layer_error * theta2) .* sigmoid_gradient([ones(size(hidden_layer_output, 1), 1) hidden_layer_input]);
    hidden_layer_error = hidden_layer_error(:, 2:end);
    delta1 = hidden_layer_error' * input_data_with_bias;
    delta2 = output_layer_error' * hidden_layer_output_with_bias;
    theta1 = theta1 - (learning_rate * delta1);
    theta2 = theta2 - (learning_rate * delta2);
end

% 测试模型
test_data = [0 0; 0 1; 1 0; 1 1];
test_data_with_bias = [ones(size(test_data, 1), 1) test_data];
hidden_layer_input = test_data_with_bias * theta1';
hidden_layer_output = sigmoid(hidden_layer_input);
hidden_layer_output_with_bias = [ones(size(hidden_layer_output, 1), 1) hidden_layer_output];
output_layer_input = hidden_layer_output_with_bias * theta2';
output_layer_output = sigmoid(output_layer_input);
disp(output_layer_output);

其中，`sigmoid` 和 `sigmoid_gradient` 函数分别为 sigmoid 函数和 sigmoid 函数的导数，其实现如下：

function result = sigmoid(x)
    result = 1 ./ (1 + exp(-x));
end

function result = sigmoid_gradient(x)
    result = sigmoid(x) .* (1 - sigmoid(x));
end