Spectral Clustering and Laplacian Eigenmaps

This lecture covers advanced machine learning techniques focusing on spectral clustering and Laplacian eigenmaps. Spectral methods decompose the Graph Laplacian matrix to identify non-linear manifolds in data. By constructing a similarity graph and measuring distances, spectral clustering can determine the number of clusters in a dataset. The eigenvalue decomposition of the Laplacian matrix plays a crucial role in identifying connected components and clustering. Laplacian eigenmaps and Isomap are discussed as non-linear embedding methods, highlighting the importance of geodesic distances in capturing data relationships. The lecture concludes with a summary of spectral methods, emphasizing the power of spectral clustering and Laplacian embeddings when the kernel is well chosen.