bp神经网络matlab实例

以下是一个 BP 神经网络的 MATLAB 实例：

假设我们需要训练一个 BP 神经网络来预测一个人的体重，基于他们的身高和年龄。我们有一个包含 1000 个样本的数据集，其中每个样本都具有身高和年龄这两个特征，以及一个对应的目标体重。我们可以将这个问题看作是一个回归问题，因为我们需要预测连续的数值输出。

首先，我们需要将数据集分成训练集和测试集：

% Load the dataset
load('weight_dataset.mat');

% Split the dataset into training and testing sets
train_ratio = 0.8;
[trainInd,testInd] = dividerand(size(X,2),train_ratio,1-train_ratio);

X_train = X(:,trainInd);
Y_train = Y(:,trainInd);

X_test = X(:,testInd);
Y_test = Y(:,testInd);

然后，我们需要定义 BP 神经网络的结构和超参数：

% Define the number of input, hidden, and output units
input_units = size(X_train,1);
hidden_units = 10;
output_units = 1;

% Define the learning rate and number of epochs
learning_rate = 0.01;
num_epochs = 1000;

接下来，我们需要初始化 BP 神经网络的权重和偏差：

% Initialize the weights and biases
W1 = rand(hidden_units,input_units);
b1 = rand(hidden_units,1);

W2 = rand(output_units,hidden_units);
b2 = rand(output_units,1);

然后，我们可以开始训练 BP 神经网络：

% Train the neural network
for i = 1:num_epochs
    % Forward propagation
    A1 = sigmoid(W1*X_train + b1);
    A2 = W2*A1 + b2;
    
    % Compute the loss
    error = Y_train - A2;
    loss = 0.5*mean(error.^2);
    
    % Backward propagation
    dA2 = -error;
    dW2 = (1/size(X_train,2))*dA2*A1';
    db2 = (1/size(X_train,2))*sum(dA2,2);
    
    dA1 = W2'*dA2.*sigmoid_gradient(A1);
    dW1 = (1/size(X_train,2))*dA1*X_train';
    db1 = (1/size(X_train,2))*sum(dA1,2);
    
    % Update the weights and biases
    W2 = W2 - learning_rate*dW2;
    b2 = b2 - learning_rate*db2;
    
    W1 = W1 - learning_rate*dW1;
    b1 = b1 - learning_rate*db1;
    
    % Print the loss every 100 epochs
    if mod(i,100) == 0
        fprintf('Epoch %d, loss = %f\n', i, loss);
    end
end

最后，我们可以使用训练好的 BP 神经网络来进行预测：

% Use the neural network to make predictions
A1_test = sigmoid(W1*X_test + b1);
A2_test = W2*A1_test + b2;

% Compute the test loss
error_test = Y_test - A2_test;
loss_test = 0.5*mean(error_test.^2);

fprintf('Test loss = %f\n', loss_test);

完整的代码如下所示：

% Load the dataset
load('weight_dataset.mat');

% Split the dataset into training and testing sets
train_ratio = 0.8;
[trainInd,testInd] = dividerand(size(X,2),train_ratio,1-train_ratio);

X_train = X(:,trainInd);
Y_train = Y(:,trainInd);

X_test = X(:,testInd);
Y_test = Y(:,testInd);

% Define the number of input, hidden, and output units
input_units = size(X_train,1);
hidden_units = 10;
output_units = 1;

% Define the learning rate and number of epochs
learning_rate = 0.01;
num_epochs = 1000;

% Initialize the weights and biases
W1 = rand(hidden_units,input_units);
b1 = rand(hidden_units,1);

W2 = rand(output_units,hidden_units);
b2 = rand(output_units,1);

% Train the neural network
for i = 1:num_epochs
    % Forward propagation
    A1 = sigmoid(W1*X_train + b1);
    A2 = W2*A1 + b2;
    
    % Compute the loss
    error = Y_train - A2;
    loss = 0.5*mean(error.^2);
    
    % Backward propagation
    dA2 = -error;
    dW2 = (1/size(X_train,2))*dA2*A1';
    db2 = (1/size(X_train,2))*sum(dA2,2);
    
    dA1 = W2'*dA2.*sigmoid_gradient(A1);
    dW1 = (1/size(X_train,2))*dA1*X_train';
    db1 = (1/size(X_train,2))*sum(dA1,2);
    
    % Update the weights and biases
    W2 = W2 - learning_rate*dW2;
    b2 = b2 - learning_rate*db2;
    
    W1 = W1 - learning_rate*dW1;
    b1 = b1 - learning_rate*db1;
    
    % Print the loss every 100 epochs
    if mod(i,100) == 0
        fprintf('Epoch %d, loss = %f\n', i, loss);
    end
end

% Use the neural network to make predictions
A1_test = sigmoid(W1*X_test + b1);
A2_test = W2*A1_test + b2;

% Compute the test loss
error_test = Y_test - A2_test;
loss_test = 0.5*mean(error_test.^2);

fprintf('Test loss = %f\n', loss_test);

% Define the sigmoid function and its derivative
function y = sigmoid(x)
    y = 1./(1 + exp(-x));
end

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