Kernel Methods for Machine Learning

This group research project explores Kernel Principal Component Analysis (KPCA), a nonlinear extension of Principal Component Analysis (PCA) for dimensionality reduction. The project develops the mathematical foundations of PCA before introducing kernel methods, which allow PCA to capture nonlinear structures in complex, high-dimensional data.

The study applies KPCA to the Olivetti Faces and MNIST datasets, investigating its use for image classification and reconstruction. Different kernel functions and hyperparameters are explored, with the performance of KPCA compared against standard PCA to assess when nonlinear dimensionality reduction can provide an advantage.