Weighted Embeddings for Low-Dimensional Graph Representation
- URL: http://arxiv.org/abs/2410.06042v1
- Date: Tue, 8 Oct 2024 13:41:03 GMT
- Title: Weighted Embeddings for Low-Dimensional Graph Representation
- Authors: Thomas Bläsius, Jean-Pierre von der Heydt, Maximilian Katzmann, Nikolai Maas,
- Abstract summary: We propose embedding a graph into a weighted space, which is closely related to hyperbolic geometry but mathematically simpler.
We show that our weighted embeddings heavily outperform state-of-the-art Euclidean embeddings for heterogeneous graphs while using fewer dimensions.
- Score: 0.13499500088995461
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent observations indicate that hyperbolic geometry is better suited to represent hierarchical information and heterogeneous data (e.g., graphs with a scale-free degree distribution). Despite their potential for more accurate representations, hyperbolic embeddings also have downsides like being more difficult to compute and harder to use in downstream tasks. We propose embedding into a weighted space, which is closely related to hyperbolic geometry but mathematically simpler. We provide the embedding algorithm WEmbed and demonstrate, based on generated as well as over 2000 real-world graphs, that our weighted embeddings heavily outperform state-of-the-art Euclidean embeddings for heterogeneous graphs while using fewer dimensions. The running time of WEmbed and embedding quality for the remaining instances is on par with state-of-the-art Euclidean embedders.
Related papers
- Shedding Light on Problems with Hyperbolic Graph Learning [2.3743504594834635]
Recent papers in the graph machine learning literature have introduced a number of approaches for hyperbolic representation learning.
We take a careful look at the field of hyperbolic graph representation learning as it stands today.
We find that a number of papers fail to diligently present baselines, make faulty modelling assumptions when constructing algorithms, and use misleading metrics to quantify geometry of graph datasets.
arXiv Detail & Related papers (2024-11-11T03:12:41Z) - Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding [51.75091298017941]
This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) for attributed graph data.
The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets.
arXiv Detail & Related papers (2024-01-12T17:57:07Z) - Improving embedding of graphs with missing data by soft manifolds [51.425411400683565]
The reliability of graph embeddings depends on how much the geometry of the continuous space matches the graph structure.
We introduce a new class of manifold, named soft manifold, that can solve this situation.
Using soft manifold for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets.
arXiv Detail & Related papers (2023-11-29T12:48:33Z) - Alignment and Outer Shell Isotropy for Hyperbolic Graph Contrastive
Learning [69.6810940330906]
We propose a novel contrastive learning framework to learn high-quality graph embedding.
Specifically, we design the alignment metric that effectively captures the hierarchical data-invariant information.
We show that in the hyperbolic space one has to address the leaf- and height-level uniformity which are related to properties of trees.
arXiv Detail & Related papers (2023-10-27T15:31:42Z) - Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of
the Same Coin [49.12496652756007]
We show that the best few-shot results are attained for hyperbolic embeddings at a common hyperbolic radius.
In contrast to prior benchmark results, we demonstrate that better performance can be achieved by a fixed-radius encoder equipped with the Euclidean metric.
arXiv Detail & Related papers (2023-09-18T14:51:46Z) - Tight and fast generalization error bound of graph embedding in metric
space [54.279425319381374]
We show that graph embedding in non-Euclidean metric space can outperform that in Euclidean space with much smaller training data than the existing bound has suggested.
Our new upper bound is significantly tighter and faster than the existing one, which can be exponential to $R$ and $O(frac1S)$ at the fastest.
arXiv Detail & Related papers (2023-05-13T17:29:18Z) - Node-Specific Space Selection via Localized Geometric Hyperbolicity in
Graph Neural Networks [38.7842803074593]
Many graph neural networks have been developed to learn graph representations in either Euclidean or hyperbolic space.
In this paper, we analyze two notions of local hyperbolicity, describing the underlying local geometry.
We show that our model Joint Space Graph Neural Network (JSGNN) can leverage both Euclidean and hyperbolic spaces during learning.
arXiv Detail & Related papers (2023-03-03T06:04:42Z) - Hyperbolic Graph Representation Learning: A Tutorial [39.25873010585029]
This tutorial aims to give an introduction to this emerging field of graph representation learning with the express purpose of being accessible to all audiences.
We first give a brief introduction to graph representation learning as well as some preliminaryian and hyperbolic geometry.
We then comprehensively revisit the technical details of the current hyperbolic graph neural networks by unifying them into a general framework.
arXiv Detail & Related papers (2022-11-08T07:15:29Z) - Geometry Contrastive Learning on Heterogeneous Graphs [50.58523799455101]
This paper proposes a novel self-supervised learning method, termed as Geometry Contrastive Learning (GCL)
GCL views a heterogeneous graph from Euclidean and hyperbolic perspective simultaneously, aiming to make a strong merger of the ability of modeling rich semantics and complex structures.
Extensive experiments on four benchmarks data sets show that the proposed approach outperforms the strong baselines.
arXiv Detail & Related papers (2022-06-25T03:54:53Z) - Enhancing Hyperbolic Graph Embeddings via Contrastive Learning [7.901082408569372]
We propose a novel Hyperbolic Graph Contrastive Learning (HGCL) framework which learns node representations through multiple hyperbolic spaces.
Experimental results on multiple real-world datasets demonstrate the superiority of the proposed HGCL.
arXiv Detail & Related papers (2022-01-21T06:10:05Z)
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.