Partitioning Well-Clustered Graphs: Spectral Clustering Works!
published: Aug. 20, 2015, recorded: July 2015, views: 1621
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
In this work we study the widely used spectral clustering algorithms, i.e. partition a graph into k clusters via (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and (2) partitioning embedded points via k-means algorithms. We show that, for a wide class of well-clustered graphs, spectral clustering algorithms can give a good approximation of the optimal clustering. To the best of our knowledge, it is the first theoretical analysis of spectral clustering algorithms for a wide family of graphs, even though such approach was proposed in the early 1990s and has comprehensive applications. We also give a nearly-linear time algorithm for partitioning well-clustered graphs, which is based on heat kernel embeddings and approximate nearest neighbor data structures.
Download slides: colt2015_zanetti_spectral_clustering_01.pdf (451.6 KB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !