A Provable Generalized Tensor Spectral Method for Uniform Hypergraph Partitioning
published: Sept. 27, 2015, recorded: July 2015, views: 1710
Download slides: icml2015_ghoshdastidar_tensor_spectral_method_01.pdf (2.0 MB)
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.
Matrix spectral methods play an important role in statistics and machine learning, and most often the word `matrix’ is dropped as, by default, one assumes that similarities or affinities are measured between two points, thereby resulting in similarity matrices. However, recent challenges in computer vision and text mining have necessitated the use of multi-way affinities in the learning methods, and this has led to a considerable interest in hypergraph partitioning methods in machine learning community. A plethora of “higher-order” algorithms have been proposed in the past decade, but their theoretical guarantees are not well-studied. In this paper, we develop a unified approach for partitioning uniform hypergraphs by means of a tensor trace optimization problem involving the affinity tensor, and a number of existing higher-order methods turn out to be special cases of the proposed formulation. We further propose an algorithm to solve the proposed trace optimization problem, and prove that it is consistent under a planted hypergraph model. We also provide experimental results to validate our theoretical findings.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !