Regression and Prediction on 2D Function Datasets: Mexican Hat, Gabor, Friedman, and Polynomial

Multiple machine learning algorithms including Multilayer Perceptron (MLP) trained with Backpropagation algorithm, Radial Basis Function Network (RBF Network), and Support Vector Machine (SVM) are employed for regression and prediction tasks on various 2D function datasets such as Mexican Hat, Gabor, Friedman, and Polynomial functions. These algorithms train on datasets to learn underlying relationships and utilize the learned models to make predictions on unseen data. The Multilayer Perceptron (MLP) employs the Backpropagation algorithm for training, where gradient descent optimization minimizes the loss function through weight adjustments. With multiple hidden layers and activation functions like ReLU or sigmoid, MLP can capture complex nonlinear relationships through iterative forward and backward passes. Radial Basis Function Network (RBF Network) utilizes radial basis functions (typically Gaussian functions) as activation functions in the hidden layer. The network calculates distances between input vectors and center points, making it particularly effective for learning complex data distributions through localized approximations. Support Vector Machine (SVM) operates by finding the optimal hyperplane that maximizes the margin between different classes using kernel functions (linear, polynomial, or RBF). For regression tasks (Support Vector Regression), SVM minimizes the error while maintaining the maximum margin boundary. These algorithms play crucial roles in regression and prediction applications, providing powerful tools for data analysis and machine learning implementations. Code implementations typically involve parameter tuning, kernel selection for SVM, hidden layer configuration for MLP, and center selection methods for RBF networks to optimize performance on specific function datasets.