Abstract
Knowledge Graph Embeddings (KGE) are used for representation learning in Knowledge Graphs (KGs) by measuring the likelihood of a relation between nodes. Rotation-based approaches, specially axis-angle representations, were shown to improve the performance of many Machine Learning (ML)-based models in different tasks including link prediction. There is a perceived disconnect between the topics of KGE models and axis-angle rotation-based approaches. This is particularly visible when considering the ability of KGEs to learn relational patterns such as symmetry, inversion, implication, equivalence, composition, and reflexivity considering axis-angle rotation-based approaches. In this article, we propose RodE, a new KGE model which employs an axis-angle representation for rotations based on Rodrigues' formula. RodE inherits the main advantages of 3-dimensional rotation from angle, orientation and distance preservation in the embedding space. Thus, the model efficiently captures the similarity between the nodes in a graph in the vector space. Our experiments show that RodE outperforms state-of-the-art models on standard datasets.
Highlights
IntroductionN -DIMENSIONAL rotations have been used for several AI-based applications such as motion detection in computer vision and kinematics descriptions in robotics
N -DIMENSIONAL rotations have been used for several AI-based applications such as motion detection in computer vision and kinematics descriptions in robotics. Such rotations have been recently employed in the development of Machine Learning (ML) models resulting in powerful learners for neural networks [8], spectral clustering [16], regression [35], ensemble learning [26], and representation learning in knowledge graphs (KGs) [28]
We focus on Knowledge Graph Embedding (KGE) models as one of the most used techniques for this problem
Summary
N -DIMENSIONAL rotations have been used for several AI-based applications such as motion detection in computer vision and kinematics descriptions in robotics. Such rotations have been recently employed in the development of ML models resulting in powerful learners for neural networks [8], spectral clustering [16], regression [35], ensemble learning [26], and representation learning in knowledge graphs (KGs) [28]. Different representations [1], [22] for three-dimensional rotations can be selected per application such as Euler angles [6], axis-angle representation (Rodrigues formula) [9], exponential coordinates [12], and matrices [25]. Each of these rotation-based approaches have specific characteristics in preserving distance, angle and orientation of the rotated
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