Inhomogeneous Hypergraph Clustering with Applications

09/05/2017
by   Pan Li, et al.
0

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 8

09/18/2019

Hypergraph partitions

We suggest a reduction of the combinatorial problem of hypergraph partit...
10/26/2018

HYPE: Massive Hypergraph Partitioning with Neighborhood Expansion

Many important real-world applications-such as social networks or distri...
10/18/2017

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

Multilevel partitioning methods that are inspired by principles of multi...
04/20/2022

Counting and enumerating optimum cut sets for hypergraph k-partitioning problems for fixed k

We consider the problem of enumerating optimal solutions for two hypergr...
09/09/2019

Hypergraph Partitioning With Embeddings

The problem of placing circuits on a chip or distributing sparse matrix ...
02/21/2016

Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques

In a series of recent works, we have generalised the consistency results...
12/28/2018

Hypergraph Clustering: A Modularity Maximization Approach

Clustering on hypergraphs has been garnering increased attention with po...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.