Spectral Clustering: Theory and Applications

This lecture covers the theory and applications of spectral clustering, starting with the notion of spectral decomposition and its application in clustering non-linear manifolds. The instructor explains the process of eigenvalue decomposition in PCA and Kernel PCA, highlighting the generation of partitions in the space. The lecture also delves into the construction of the Laplacian matrix and its role in identifying connected components in a graph. Practical exercises demonstrate the steps involved in spectral clustering, including building similarity graphs, measuring distances, and identifying clusters. The lecture concludes with a discussion on the equivalency of spectral clustering to other non-linear embeddings and the use of Kernel PCA as a pre-processing step before kernel K-means.