Dist2Cycle: A Simplicial Neural Network for Homology Localization
- URL: http://arxiv.org/abs/2110.15182v1
- Date: Thu, 28 Oct 2021 14:59:41 GMT
- Title: Dist2Cycle: A Simplicial Neural Network for Homology Localization
- Authors: Alexandros Dimitrios Keros, Vidit Nanda, Kartic Subr
- Abstract summary: Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations.
We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
- Score: 66.15805004725809
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Simplicial complexes can be viewed as high dimensional generalizations of
graphs that explicitly encode multi-way ordered relations between vertices at
different resolutions, all at once. This concept is central towards detection
of higher dimensional topological features of data, features to which graphs,
encoding only pairwise relationships, remain oblivious. While attempts have
been made to extend Graph Neural Networks (GNNs) to a simplicial complex
setting, the methods do not inherently exploit, or reason about, the underlying
topological structure of the network. We propose a graph convolutional model
for learning functions parametrized by the $k$-homological features of
simplicial complexes. By spectrally manipulating their combinatorial
$k$-dimensional Hodge Laplacians, the proposed model enables learning
topological features of the underlying simplicial complexes, specifically, the
distance of each $k$-simplex from the nearest "optimal" $k$-th homology
generator, effectively providing an alternative to homology localization.
Related papers
- Simplicial Representation Learning with Neural $k$-Forms [14.566552361705499]
This paper focuses on leveraging geometric information from simplicial complexes embedded in $mathbbRn$ using node coordinates.
We use differential k-forms in mathbbRn to create representations of simplices, offering interpretability and geometric consistency without message passing.
Our method is efficient, versatile, and applicable to various input complexes, including graphs, simplicial complexes, and cell complexes.
arXiv Detail & Related papers (2023-12-13T21:03:39Z) - Algebraic Topological Networks via the Persistent Local Homology Sheaf [15.17547132363788]
We introduce a novel approach to enhance graph convolution and attention modules by incorporating local topological properties of the data.
We consider the framework of sheaf neural networks, which has been previously leveraged to incorporate additional structure into graph neural networks' features.
arXiv Detail & Related papers (2023-11-16T19:24:20Z) - Generalized Simplicial Attention Neural Networks [22.171364354867723]
We introduce Generalized Simplicial Attention Neural Networks (GSANs)
GSANs process data living on simplicial complexes using masked self-attentional layers.
These schemes learn how to combine data associated with neighbor simplices of consecutive order in a task-oriented fashion.
arXiv Detail & Related papers (2023-09-05T11:29:25Z) - Torsion Graph Neural Networks [21.965704710488232]
We propose TorGNN, an analytic torsion enhanced Graph Neural Network model.
In our TorGNN, for each edge, a corresponding local simplicial complex is identified, then the analytic torsion is calculated.
It has been found that our TorGNN can achieve superior performance on both tasks, and outperform various state-of-the-art models.
arXiv Detail & Related papers (2023-06-23T15:02:23Z) - Relation Embedding based Graph Neural Networks for Handling
Heterogeneous Graph [58.99478502486377]
We propose a simple yet efficient framework to make the homogeneous GNNs have adequate ability to handle heterogeneous graphs.
Specifically, we propose Relation Embedding based Graph Neural Networks (RE-GNNs), which employ only one parameter per relation to embed the importance of edge type relations and self-loop connections.
arXiv Detail & Related papers (2022-09-23T05:24:18Z) - Simple and Efficient Heterogeneous Graph Neural Network [55.56564522532328]
Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations.
Existing HGNNs inherit many mechanisms from graph neural networks (GNNs) over homogeneous graphs, especially the attention mechanism and the multi-layer structure.
This paper conducts an in-depth and detailed study of these mechanisms and proposes Simple and Efficient Heterogeneous Graph Neural Network (SeHGNN)
arXiv Detail & Related papers (2022-07-06T10:01:46Z) - Heterogeneous Graph Neural Networks using Self-supervised Reciprocally
Contrastive Learning [102.9138736545956]
Heterogeneous graph neural network (HGNN) is a very popular technique for the modeling and analysis of heterogeneous graphs.
We develop for the first time a novel and robust heterogeneous graph contrastive learning approach, namely HGCL, which introduces two views on respective guidance of node attributes and graph topologies.
In this new approach, we adopt distinct but most suitable attribute and topology fusion mechanisms in the two views, which are conducive to mining relevant information in attributes and topologies separately.
arXiv Detail & Related papers (2022-04-30T12:57:02Z) - Heterogeneous Graph Neural Network with Multi-view Representation
Learning [16.31723570596291]
We propose a Heterogeneous Graph Neural Network with Multi-View Representation Learning (MV-HetGNN) for heterogeneous graph embedding.
The proposed model consists of node feature transformation, view-specific ego graph encoding and auto multi-view fusion to thoroughly learn complex structural and semantic information for generating comprehensive node representations.
Extensive experiments on three real-world heterogeneous graph datasets show that the proposed MV-HetGNN model consistently outperforms all the state-of-the-art GNN baselines in various downstream tasks.
arXiv Detail & Related papers (2021-08-31T07:18:48Z) - Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals.
We propose a general graph estimator based on a novel structured fusion regularization.
We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
arXiv Detail & Related papers (2021-03-05T04:42:32Z) - Building powerful and equivariant graph neural networks with structural
message-passing [74.93169425144755]
We propose a powerful and equivariant message-passing framework based on two ideas.
First, we propagate a one-hot encoding of the nodes, in addition to the features, in order to learn a local context matrix around each node.
Second, we propose methods for the parametrization of the message and update functions that ensure permutation equivariance.
arXiv Detail & Related papers (2020-06-26T17:15:16Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.