TopER: Topological Embeddings in Graph Representation Learning
- URL: http://arxiv.org/abs/2410.01778v2
- Date: Thu, 3 Oct 2024 01:58:26 GMT
- Title: TopER: Topological Embeddings in Graph Representation Learning
- Authors: Astrit Tola, Funmilola Mary Taiwo, Cuneyt Gurcan Akcora, Baris Coskunuzer,
- Abstract summary: Topological Evolution Rate (TopER) is a low-dimensional embedding approach grounded in topological data analysis.
TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures.
Our models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.
- Score: 8.052380377159398
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting interpretability and practical visualization. In this work, we introduce Topological Evolution Rate (TopER), a novel, low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures, resulting in intuitive and interpretable visualizations of graph data. This approach not only enhances the exploration of graph datasets but also delivers competitive performance in graph clustering and classification tasks. Our TopER-based models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.
Related papers
- GraphGLOW: Universal and Generalizable Structure Learning for Graph
Neural Networks [72.01829954658889]
This paper introduces the mathematical definition of this novel problem setting.
We devise a general framework that coordinates a single graph-shared structure learner and multiple graph-specific GNNs.
The well-trained structure learner can directly produce adaptive structures for unseen target graphs without any fine-tuning.
arXiv Detail & Related papers (2023-06-20T03:33:22Z) - Bures-Wasserstein Means of Graphs [60.42414991820453]
We propose a novel framework for defining a graph mean via embeddings in the space of smooth graph signal distributions.
By finding a mean in this embedding space, we can recover a mean graph that preserves structural information.
We establish the existence and uniqueness of the novel graph mean, and provide an iterative algorithm for computing it.
arXiv Detail & Related papers (2023-05-31T11:04:53Z) - State of the Art and Potentialities of Graph-level Learning [54.68482109186052]
Graph-level learning has been applied to many tasks including comparison, regression, classification, and more.
Traditional approaches to learning a set of graphs rely on hand-crafted features, such as substructures.
Deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and encoding graphs into low-dimensional representations.
arXiv Detail & Related papers (2023-01-14T09:15:49Z) - Structure-Preserving Graph Representation Learning [43.43429108503634]
We propose a novel Structure-Preserving Graph Representation Learning (SPGRL) method to fully capture the structure information of graphs.
Specifically, to reduce the uncertainty and misinformation of the original graph, we construct a feature graph as a complementary view via k-Nearest Neighbor method.
Our method has quite superior performance on semi-supervised node classification task and excellent robustness under noise perturbation on graph structure or node features.
arXiv Detail & Related papers (2022-09-02T02:49:19Z) - Effective and Efficient Graph Learning for Multi-view Clustering [173.8313827799077]
We propose an effective and efficient graph learning model for multi-view clustering.
Our method exploits the view-similar between graphs of different views by the minimization of tensor Schatten p-norm.
Our proposed algorithm is time-economical and obtains the stable results and scales well with the data size.
arXiv Detail & Related papers (2021-08-15T13:14:28Z) - SUGAR: Subgraph Neural Network with Reinforcement Pooling and
Self-Supervised Mutual Information Mechanism [33.135006052347194]
This paper presents a novel hierarchical subgraph-level selection and embedding based graph neural network for graph classification, namely SUGAR.
SUGAR reconstructs a sketched graph by extracting striking subgraphs as the representative part of the original graph to reveal subgraph-level patterns.
To differentiate subgraph representations among graphs, we present a self-supervised mutual information mechanism to encourage subgraph embedding.
arXiv Detail & Related papers (2021-01-20T15:06:16Z) - CommPOOL: An Interpretable Graph Pooling Framework for Hierarchical
Graph Representation Learning [74.90535111881358]
We propose a new interpretable graph pooling framework - CommPOOL.
It can capture and preserve the hierarchical community structure of graphs in the graph representation learning process.
CommPOOL is a general and flexible framework for hierarchical graph representation learning.
arXiv Detail & Related papers (2020-12-10T21:14:18Z) - GraphOpt: Learning Optimization Models of Graph Formation [72.75384705298303]
We propose an end-to-end framework that learns an implicit model of graph structure formation and discovers an underlying optimization mechanism.
The learned objective can serve as an explanation for the observed graph properties, thereby lending itself to transfer across different graphs within a domain.
GraphOpt poses link formation in graphs as a sequential decision-making process and solves it using maximum entropy inverse reinforcement learning algorithm.
arXiv Detail & Related papers (2020-07-07T16:51:39Z) - Quantifying Challenges in the Application of Graph Representation
Learning [0.0]
We provide an application oriented perspective to a set of popular embedding approaches.
We evaluate their representational power with respect to real-world graph properties.
Our results suggest that "one-to-fit-all" GRL approaches are hard to define in real-world scenarios.
arXiv Detail & Related papers (2020-06-18T03:19:43Z) - Deep Graph Mapper: Seeing Graphs through the Neural Lens [4.401427499962144]
We merge Mapper with the expressive power of Graph Neural Networks (GNNs) to produce hierarchical, topologically-grounded visualisations of graphs.
These visualisations do not only help discern the structure of complex graphs but also provide a means of understanding the models applied to them for solving various tasks.
arXiv Detail & Related papers (2020-02-10T15:29:09Z)
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.