Motif Learning in Knowledge Graphs Using Trajectories Of Differential Equations

• URL: http://arxiv.org/abs/2010.06684v2
• Date: Sun, 18 Oct 2020 18:31:11 GMT
• Title: Motif Learning in Knowledge Graphs Using Trajectories Of Differential Equations
• Authors: Mojtaba Nayyeri, Chengjin Xu, Jens Lehmann, Sahar Vahdati
• Abstract summary: Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks. Many KGEs use the flat geometry which renders them incapable of preserving complex structures. We propose a neuro differential KGE that embeds nodes of a KG on the trajectories of Ordinary Differential Equations (ODEs)
• Score: 14.279419014064047
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a knowledge graph into a geometric space (usually a vector space). Ultimately, the plausibility of the predicted links is measured by using a scoring function over the learned embeddings (vectors). Therefore, the capability in preserving graph characteristics including structural aspects and semantics highly depends on the design of the KGE, as well as the inherited abilities from the underlying geometry. Many KGEs use the flat geometry which renders them incapable of preserving complex structures and consequently causes wrong inferences by the models. To address this problem, we propose a neuro differential KGE that embeds nodes of a KG on the trajectories of Ordinary Differential Equations (ODEs). To this end, we represent each relation (edge) in a KG as a vector field on a smooth Riemannian manifold. We specifically parameterize ODEs by a neural network to represent various complex shape manifolds and more importantly complex shape vector fields on the manifold. Therefore, the underlying embedding space is capable of getting various geometric forms to encode complexity in subgraph structures with different motifs. Experiments on synthetic and benchmark dataset as well as social network KGs justify the ODE trajectories as a means to structure preservation and consequently avoiding wrong inferences over state-of-the-art KGE models.

Related papers

• A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems [87.30652640973317]
  Recent advances in computational modelling of atomic systems represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. This paper provides a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems.
  arXiv  Detail & Related papers  (2023-12-12T18:44:19Z)
• 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)
• FMGNN: Fused Manifold Graph Neural Network [102.61136611255593]
  Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. We propose the Fused Manifold Graph Neural Network (NN), a novel GNN architecture that embeds graphs into different Manifolds during training. Our experiments demonstrate that NN yields superior performance over strong baselines on the benchmarks of node classification and link prediction tasks.
  arXiv  Detail & Related papers  (2023-04-03T15:38:53Z)
• Latent Graph Inference using Product Manifolds [0.0]
  We generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.
  arXiv  Detail & Related papers  (2022-11-26T22:13:06Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  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.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• Hermitian Symmetric Spaces for Graph Embeddings [0.0]
  We learn continuous representations of graphs in spaces of symmetric matrices over C. These spaces offer a rich geometry that simultaneously admits hyperbolic and Euclidean subspaces. The proposed models are able to automatically adapt to very dissimilar arrangements without any apriori estimates of graph features.
  arXiv  Detail & Related papers  (2021-05-11T18:14:52Z)
• Knowledge Graph Embeddings in Geometric Algebras [14.269860621624392]
  We introduce a novel geometric algebra-based KG embedding framework, GeomE. Our framework subsumes several state-of-the-art KG embedding approaches and is advantageous with its ability of modeling various key relation patterns. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.
  arXiv  Detail & Related papers  (2020-10-02T13:36:24Z)
• 5* Knowledge Graph Embeddings with Projective Transformations [13.723120574076127]
  We present a novel knowledge graph embedding model (5*E) in projective geometry. It supports multiple simultaneous transformations - specifically inversion, reflection, translation, rotation, and homothety. It outperforms existing approaches on the most widely used link prediction benchmarks.
  arXiv  Detail & Related papers  (2020-06-08T23:28:07Z)
• Embedding Graph Auto-Encoder for Graph Clustering [90.8576971748142]
  Graph auto-encoder (GAE) models are based on semi-supervised graph convolution networks (GCN) We design a specific GAE-based model for graph clustering to be consistent with the theory, namely Embedding Graph Auto-Encoder (EGAE) EGAE consists of one encoder and dual decoders.
  arXiv  Detail & Related papers  (2020-02-20T09:53:28Z)

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.