MATLAB Implementation of Backpropagation Neural Network

Backpropagation (BP) neural network is an artificial neural network model widely used for pattern recognition and function fitting. When implementing BP neural networks in MATLAB, users can flexibly set the number of hidden layers and neurons in each layer to adapt to different task requirements.

### 1. Network Architecture BP neural networks typically consist of an input layer, hidden layers, and an output layer. The input layer receives external data, hidden layers perform feature extraction and nonlinear transformations, while the output layer generates final predictions. The number of hidden layers and neurons can be adjusted according to problem complexity. Key MATLAB functions include `feedforwardnet` for network creation and `configure` for layer-specific settings.

### 2. Training Process BP neural network training primarily involves the following steps: Forward Propagation: Input data is processed layer by layer until obtaining output layer predictions, implemented using matrix multiplication and activation functions. Error Calculation: Mean squared error or other loss functions compare predictions with actual values using functions like `mse` or `crossentropy`. Backpropagation: Error signals propagate backward from output to input layers, calculating gradients through chain rule differentiation. Weight Update: Gradient descent or optimization algorithms update network parameters using functions like `trainlm` (Levenberg-Marquardt) or `traingd` (standard gradient descent).

### 3. MATLAB Implementation Key Points Data Preprocessing: Input data requires normalization or standardization using `mapminmax` or `zscore` functions to improve training efficiency. Activation Function Selection: Hidden layers typically use Sigmoid, ReLU, or Tanh functions (`tansig`, `purelin`), while output layers employ linear or Softmax activation depending on task requirements. Training Parameter Adjustment: Learning rate, iteration count (`net.trainParam.epochs`), and target error (`net.trainParam.goal`) require careful configuration to prevent overfitting or underfitting using validation techniques.

By optimizing the number of hidden layers and neurons through methods like grid search or Bayesian optimization, network performance can be enhanced for better adaptation to classification or regression tasks.