BP Algorithm and Momentum-Adaptive Learning Rate Adjustment Algorithm (Improved BP Algorithm) Programs

This article presents two MATLAB implementations: a standard Backpropagation (BP) algorithm program and an enhanced Momentum-Adaptive Learning Rate Adjustment algorithm (Improved BP algorithm) program. These implementations are designed to facilitate advanced data analysis and predictive modeling. The BP algorithm employs gradient descent with error backpropagation to adjust neural network weights, effectively minimizing model errors through iterative weight updates calculated via chain rule differentiation. The Improved BP algorithm incorporates momentum-based optimization and adaptive learning rate adjustment, dynamically modifying the learning rate using techniques like gradient magnitude monitoring or epoch-based decay schedules to accelerate convergence and prevent overshooting in complex datasets. Both programs feature modular MATLAB code structures with configurable parameters including hidden layer sizes, activation functions (sigmoid/tanh/ReLU), and termination criteria. Implementation involves initializing network weights, forward propagation for output calculation, error computation using loss functions (MSE/cross-entropy), and backward propagation for gradient calculations. Users can execute these programs by loading dataset matrices, setting hyperparameters, and running the training loops, which include batch processing and convergence monitoring through validation checks. These tools significantly enhance prediction accuracy in research and industrial applications by providing robust neural network training frameworks with detailed error tracking and performance visualization capabilities.