Learning on Hypergraphs with Sparsity

04/03/2018
by   Canh Hao Nguyen, et al.
0

Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, one wishes to learn a smooth function with respect to its topology. A fundamental issue is to find suitable smoothness measures of functions on the nodes of a graph/hypergraph. We show a general framework that generalizes previously proposed smoothness measures and also gives rise to new ones. To address the problem of irrelevant or noisy data, we wish to incorporate sparse learning framework into learning on hypergraphs. We propose sparsely smooth formulations that learn smooth functions and induce sparsity on hypergraphs at both hyperedge and node levels. We show their properties and sparse support recovery results. We conduct experiments to show that our sparsely smooth models have benefits to irrelevant and noisy data, and usually give similar or improved performances compared to dense models.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

01/23/2019

Hypergraph Convolution and Hypergraph Attention

Recently, graph neural networks have attracted great attention and achie...
06/15/2021

Hypergraph Dissimilarity Measures

In this paper, we propose two novel approaches for hypergraph comparison...
06/10/2021

Learnable Hypergraph Laplacian for Hypergraph Learning

HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated thei...
02/19/2021

Regularized Recovery by Multi-order Partial Hypergraph Total Variation

Capturing complex high-order interactions among data is an important tas...
06/24/2021

You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks

Hypergraphs are used to model higher-order interactions amongst agents a...
01/09/2020

Hypergraph Cuts with General Splitting Functions

The minimum s-t cut problem in graphs is one of the most fundamental pro...
03/18/2016

Geometric Hypergraph Learning for Visual Tracking

Graph based representation is widely used in visual tracking field by fi...
This week in AI

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