Three-Layer Backpropagation Neural Network Algorithm

Backpropagation Neural Network (BPNN) is a classic supervised learning algorithm widely applied in pattern recognition, predictive analysis, and other domains. The three-layer architecture consists of an input layer, hidden layer, and output layer, enabling self-learning optimization through an error backpropagation mechanism.

Core Logic Forward Propagation: The input layer receives data and transmits weighted signals to the hidden layer. The hidden layer processes these signals using an activation function (e.g., Sigmoid or ReLU) before forwarding them to the output layer. The output layer computes predictions and evaluates errors against ground truth values using loss functions like Mean Squared Error (MSE) for regression or Cross-Entropy for classification.

Backward Propagation: Errors propagate backward from the output layer. Gradients for weights and biases are calculated layer by layer via the chain rule of differentiation. Optimization methods like Gradient Descent (or variants such as Momentum or Adam) update parameters iteratively to minimize error.

MATLAB Implementation Features Matrix Operations Optimization: MATLAB's built-in matrix operations efficiently handle batch data processing during forward/backward propagation, reducing loop overhead. Adaptive Learning Rate: Implementations can dynamically adjust learning rates (e.g., via decay schedules) to balance convergence speed and stability. Performance Monitoring: Track training error curves or validation accuracy in real-time to prevent overfitting, using tools like plot functions or early stopping callbacks.

Application Scenarios Ideal for nonlinear data modeling tasks such as time-series forecasting, classification problems, and dynamic system simulations, where it excels in capturing complex patterns.