Mitigating Heterogeneity in Factor Tensors for Improved Temporal Knowledge Graph Embedding

Kernkonzepte

Heterogeneity among factor tensors in tensor decomposition significantly hinders the tensor fusion process and limits the performance of temporal knowledge graph embedding models. Mapping factor tensors onto a unified Lie group manifold can mitigate this heterogeneity and enhance the tensor decomposition based temporal knowledge graph embedding.

Zusammenfassung

The paper investigates the negative effect of heterogeneity among factor tensors in tensor decomposition based temporal knowledge graph embedding (TKGE) models. It is observed that the inherent heterogeneity in TKGs, specifically in terms of entity, relation, and timestamp, leads to the learned factor tensors exhibiting different distributions, which limits the tensor fusion process and lowers the link prediction accuracy.
To address this issue, the authors propose a novel method that maps the factor tensors onto a unified smooth Lie group manifold. This makes the distribution of factor tensors more homogeneous, as the manifold in Lie group looks the same at every point and all tangent spaces at any point are alike. The authors provide theoretical proof that homogeneous factor tensors are more effective than heterogeneous factor tensors in approximating the target tensor for tensor decomposition based TKGE methods.
The proposed method can be directly integrated into existing tensor decomposition based TKGE models without introducing any additional parameters. Extensive experiments on ICEWS14 and ICEWS05-15 datasets demonstrate the effectiveness of the method in mitigating the heterogeneity and enhancing the performance of various tensor decomposition based TKGE models.

Statistiken

The authors report the following key statistics and figures:

The heterogeneity among entities, relations, and timestamps in TKGs is evidenced by the differing distribution curves shown in Figure 1(a).
The homogeneous distribution curves of entities, relations, and timestamps when using the proposed method are shown in Figure 1(b).
Quantitative analysis results on the difference in distance between various factor tensors for TComplEx and TNTComplEx models, before and after applying the proposed method, are presented in Table 2.

Zitate

"To the best of our knowledge, we are the first to investigate the negative effect of the heterogeneity among the factor tensors for tensor decomposition based TKGE models and propose to enhance these models by diminishing the heterogeneity via Lie group manifold."
"We provide the theoretical proof of our motivation that homogeneous factor tensors are more effective than heterogeneous factor tensors in approximating the target in TKGE."

Wichtige Erkenntnisse aus

Mitigating Heterogeneity among Factor Tensors via Lie Group Manifolds for Tensor Decomposition Based Temporal Knowledge Graph Embedding

by Jiang Li,Xia... um arxiv.org 04-16-2024

https://arxiv.org/pdf/2404.09155.pdf

Tiefere Fragen

How can the proposed method be extended to handle new entities not present in the training data

To handle new entities not present in the training data, the proposed method can be extended by incorporating techniques for entity alignment or entity linking. By leveraging external knowledge sources or entity embeddings, the model can map new entities to the existing entity space. This alignment process can help in integrating the new entities into the tensor decomposition framework, allowing the model to make predictions even for unseen entities. Additionally, techniques such as zero-shot learning or few-shot learning can be employed to generalize the model's knowledge to new entities based on their similarities to existing entities in the knowledge graph.

What other types of manifolds or geometric structures could be explored to mitigate heterogeneity in tensor decomposition based TKGE models

In addition to Lie group manifolds, other types of manifolds or geometric structures can be explored to mitigate heterogeneity in tensor decomposition based TKGE models. One potential approach is to investigate the use of Riemannian manifolds, which can capture the intrinsic geometry of the data space more effectively. By modeling the factor tensors on Riemannian manifolds, the model can account for the curvature and non-linearity of the data distribution, leading to more accurate representations. Furthermore, exploring hyperbolic spaces or graph embeddings in hyperbolic geometry can also be beneficial, especially for capturing hierarchical structures and complex relationships in knowledge graphs.

Can the insights from this work be applied to other domains beyond temporal knowledge graphs, where tensor decomposition is used for representation learning

The insights from this work can be applied to other domains beyond temporal knowledge graphs where tensor decomposition is used for representation learning. For example, in recommender systems, tensor decomposition methods are commonly used to model user-item interactions over time. By applying the proposed method to mitigate heterogeneity among factor tensors in recommender systems, the model can better capture the dynamics of user preferences and item characteristics, leading to improved recommendation accuracy. Similarly, in natural language processing tasks such as text classification or sentiment analysis, tensor decomposition techniques can benefit from addressing heterogeneity among word embeddings or document representations to enhance the performance of the models. By adapting the proposed method to these domains, the models can effectively handle the diverse semantic content and relationships present in the data.