Generalized Discriminant Analysis (GDA) via Kernel Methods

This document presents a MATLAB implementation of Generalized Discriminant Analysis (GDA) utilizing kernel methods for generalization. The GDA algorithm in this program employs kernel techniques to handle non-linearly separable data by mapping input features to higher-dimensional spaces. Kernel methods represent powerful mathematical tools widely adopted in data science and machine learning for their ability to transform complex data relationships. The implementation leverages kernel functions (such as polynomial, RBF, or sigmoid kernels) to compute similarity measures between data points without explicitly performing the high-dimensional mapping. This kernel trick allows the algorithm to operate efficiently in implicit feature spaces while maintaining computational feasibility. Through this approach, problems that are linearly inseparable in original feature spaces become solvable in transformed higher-dimensional spaces. Key implementation aspects include: - Kernel matrix computation using selected kernel functions - Eigenvalue decomposition for discriminant space projection - Dimensionality reduction while preserving class separability - Support for both linear and non-linear classification boundaries The MATLAB code provides a flexible framework for handling complex pattern recognition tasks, making data processing more adaptable and computationally efficient for real-world applications.