RBF Network Training Implementation Using Gradient Descent

This source code implements RBF network training using gradient descent method, with the algorithm being custom-developed. During the training process, the network weights and biases are first initialized. The gradient descent algorithm then iteratively adjusts these parameters to minimize the difference between the network output and target values. The implementation follows these key steps: 1. Parameter initialization for RBF centers, widths, and output layer weights 2. Forward propagation through RBF activation functions 3. Loss calculation using mean squared error (MSE) between predicted and actual outputs 4. Backward propagation to compute gradients with respect to all parameters 5. Parameter updates using the calculated gradients and learning rate In each iteration, the algorithm computes the gradient of the loss function and updates parameters according to the learning rate, which controls the step size of parameter adjustments. The training involves multiple epochs where the model processes training samples repeatedly, gradually refining parameters through gradient-based optimization. After sufficient iterations, the algorithm converges to an RBF network model that demonstrates good performance on the training dataset. Key implementation details include: - Custom gradient calculation for RBF network architecture - Learning rate scheduling for stable convergence - Iterative parameter updates using the gradient descent rule: θ = θ - α∇J(θ) - Early stopping criteria based on validation error to prevent overfitting The resulting model achieves optimal performance through systematic adjustment of RBF network parameters using fundamental optimization principles.