Backpropagation Neural Network MATLAB Implementation with Custom Source Code

Backpropagation Neural Network (BPNN) is a classic artificial neural network model widely used in machine learning tasks such as pattern recognition and function approximation. Its core principle involves adjusting network weights through the backpropagation algorithm to gradually reduce prediction errors.

Implementing BP neural networks in MATLAB without using the Neural Network Toolbox allows for deeper understanding of the algorithm's underlying mechanisms. The typical implementation workflow includes these key steps:

Network Initialization: Determine the number of nodes in input, hidden, and output layers, then randomly initialize weight matrices. In code implementation, this typically involves using functions like rand() to generate small random values for initial weights, as proper initialization significantly impacts training performance.

Forward Propagation: After inputting sample data, compute outputs layer by layer until obtaining final predictions. Implementation requires matrix multiplication operations and activation functions like Sigmoid or ReLU, where Sigmoid can be coded as 1./(1+exp(-x)) and ReLU as max(0,x).

Error Calculation: Measure the difference between predicted and actual values using loss functions such as Mean Squared Error (MSE). Code implementation involves calculating MSE = mean((y_pred - y_true).^2), which serves as the basis for subsequent weight adjustments.

Backpropagation: Starting from the output layer, compute error signals layer by layer and update weights using gradient descent. This requires calculating partial derivatives of the loss function with respect to weights (gradients), implementing chain rule computations through matrix operations and derivative calculations of activation functions.

Iterative Training: Repeat forward and backward propagation until error converges to acceptable range or reaches preset epochs. Code implementation typically uses for/while loops with convergence checks, where learning rate scheduling can be incorporated using techniques like learning rate decay.

In custom implementations, special attention should be paid to learning rate setting, activation function selection, and weight update methods. Additionally, regularization techniques or cross-validation can be implemented to prevent overfitting, such as adding L2 regularization terms to the loss function.

The advantage of manual implementation lies in high flexibility, allowing free adjustment of network architecture and training strategies to better suit specific task requirements. However, compared to toolbox approaches, it requires more debugging and optimization work, particularly in gradient checking and hyperparameter tuning.