Standard Five-Input Three-Output BP Neural Network Implementation

The standard BP (Backpropagation) neural network is a classic feedforward neural network commonly used for solving classification and regression problems. Below we demonstrate how to implement a five-input three-output network structure in MATLAB without relying on the toolbox. ### Network Architecture Description Input Layer: Contains 5 nodes corresponding to 5 input features. Hidden Layer: The number of nodes can be configured based on requirements (typically 8-10 nodes), with Sigmoid or ReLU commonly used as activation functions. Output Layer: 3 nodes corresponding to 3 output targets, typically using Sigmoid for classification tasks or linear functions for regression problems. ### Core Implementation Steps Parameter Initialization: Randomly initialize weight matrices from input-to-hidden layer and hidden-to-output layer, along with bias vectors. Forward Propagation: Calculate activation values for hidden and output layers by processing weighted sums through activation functions. Error Calculation: Compute output layer errors and propagate them backward to determine hidden layer errors. Weight Update: Adjust weights and biases using gradient descent method, with learning rate controlling the update magnitude. Iterative Training: Repeat forward propagation, error calculation, and weight update until error convergence or maximum iterations reached. ### Key Implementation Details Activation Function Selection: Hidden layers typically use Sigmoid or Tanh functions, while output layer functions should match task requirements. Learning Rate Configuration: Excessive rates cause oscillations while insufficient rates slow convergence; consider implementing dynamic adjustment strategies. Stopping Criteria: Preset error thresholds or iteration limits to prevent overfitting. ### Code Implementation Enhancements In MATLAB implementation, key operations include: - Matrix operations for efficient forward/backward propagation - Element-wise activation function application using arrayfun or direct computation - Gradient calculation through chain rule differentiation - Vectorized updates for weights and biases to optimize performance This basic BP neural network implementation suits small-scale data modeling. For enhanced performance, consider incorporating momentum terms or adaptive learning rate optimizers like Adam or RMSprop.