BP神经网络 matlab 回归举例

以下是一个简单的BP神经网络回归的例子，使用Matlab实现。

数据准备：

为了演示，我们将使用一个简单的数据集，其中包含两个变量X和Y。我们将使用这些变量来训练BP神经网络，以预测Y的值。

首先，我们需要加载数据集，将其分为训练集和测试集，并进行归一化处理。

% Load data
data = load('data.mat');

% Split data into training and testing sets
train_data = data(1:80,:);
test_data = data(81:end,:);

% Normalize data
train_data = normalize(train_data);
test_data = normalize(test_data);

网络设置：

接下来，我们需要设置神经网络的结构和参数。我们将定义一个三层的BP神经网络，其中输入层有一个神经元，隐藏层有两个神经元，输出层有一个神经元。我们将使用sigmoid函数作为激活函数，并使用均方误差作为损失函数。

% Set network parameters
input_layer_size = 1;
hidden_layer_size = 2;
output_layer_size = 1;

% Initialize network weights and biases
W1 = randn(hidden_layer_size, input_layer_size);
b1 = randn(hidden_layer_size, 1);
W2 = randn(output_layer_size, hidden_layer_size);
b2 = randn(output_layer_size, 1);

% Set learning rate and number of epochs
alpha = 0.01;
epochs = 1000;

% Set activation function and loss function
sigmoid = @(x) 1./(1+exp(-x));
mse = @(y, t) mean((y - t).^2);

训练网络：

现在我们可以开始训练网络了。在每个迭代中，我们将使用前向传播计算网络的输出，并使用反向传播来更新网络的权重和偏置。

% Train network
for i = 1:epochs
    
    % Forward propagation
    z1 = W1 * train_data(:,1)' + b1;
    a1 = sigmoid(z1);
    z2 = W2 * a1 + b2;
    y = z2;
    
    % Backward propagation
    delta2 = y - train_data(:,2)';
    delta1 = (W2' * delta2) .* a1 .* (1-a1);
    
    % Update weights and biases
    W2 = W2 - alpha * delta2 * a1';
    b2 = b2 - alpha * delta2;
    W1 = W1 - alpha * delta1 * train_data(:,1);
    b1 = b1 - alpha * delta1;
    
    % Calculate training error
    train_error = mse(y, train_data(:,2)');
    
    % Display progress
    if mod(i, 100) == 0
        fprintf('Epoch %d, Training error: %f\n', i, train_error);
    end
    
end

测试网络：

训练完成后，我们可以使用测试数据集来评估网络的性能。我们将使用前向传播计算网络的输出，并计算测试误差。

% Test network
z1 = W1 * test_data(:,1)' + b1;
a1 = sigmoid(z1);
z2 = W2 * a1 + b2;
y = z2;

% Calculate testing error
test_error = mse(y, test_data(:,2)');

% Display results
fprintf('Testing error: %f\n', test_error);

完整代码：

% Load data
data = load('data.mat');

% Split data into training and testing sets
train_data = data(1:80,:);
test_data = data(81:end,:);

% Normalize data
train_data = normalize(train_data);
test_data = normalize(test_data);

% Set network parameters
input_layer_size = 1;
hidden_layer_size = 2;
output_layer_size = 1;

% Initialize network weights and biases
W1 = randn(hidden_layer_size, input_layer_size);
b1 = randn(hidden_layer_size, 1);
W2 = randn(output_layer_size, hidden_layer_size);
b2 = randn(output_layer_size, 1);

% Set learning rate and number of epochs
alpha = 0.01;
epochs = 1000;

% Set activation function and loss function
sigmoid = @(x) 1./(1+exp(-x));
mse = @(y, t) mean((y - t).^2);

% Train network
for i = 1:epochs
    
    % Forward propagation
    z1 = W1 * train_data(:,1)' + b1;
    a1 = sigmoid(z1);
    z2 = W2 * a1 + b2;
    y = z2;
    
    % Backward propagation
    delta2 = y - train_data(:,2)';
    delta1 = (W2' * delta2) .* a1 .* (1-a1);
    
    % Update weights and biases
    W2 = W2 - alpha * delta2 * a1';
    b2 = b2 - alpha * delta2;
    W1 = W1 - alpha * delta1 * train_data(:,1);
    b1 = b1 - alpha * delta1;
    
    % Calculate training error
    train_error = mse(y, train_data(:,2)');
    
    % Display progress
    if mod(i, 100) == 0
        fprintf('Epoch %d, Training error: %f\n', i, train_error);
    end
    
end

% Test network
z1 = W1 * test_data(:,1)' + b1;
a1 = sigmoid(z1);
z2 = W2 * a1 + b2;
y = z2;

% Calculate testing error
test_error = mse(y, test_data(:,2)');

% Display results
fprintf('Testing error: %f\n', test_error);