Geometric transformations including translation, rotation, and scaling are commonly used operations in image processing. Besides, some of them are successfully used in developing effective knowledge graph embedding (KGE). Inspired by the synergy, we propose a new KGE model by leveraging all three operations in this work. Since translation, rotation, and scaling operations are cascaded to form a composite one, the new model is named CompoundE. By casting CompoundE in the framework of group theory, we show that quite a few distanced-based KGE models are special cases of CompoundE. CompoundE extends the simple distance-based scoring functions to relation-dependent compound operations on head and/or tail entities. To demonstrate the effectiveness of CompoundE, we perform three prevalent KG prediction tasks including link prediction, path query answering, and entity typing, on a range of datasets. CompoundE outperforms extant models consistently, demonstrating its effectiveness and flexibility.

Knowledge graph completion (KGC) aims to discover missing relationships between entities in knowledge graphs (KGs). Most prior KGC work focuses on learning embeddings for entities and relations through a simple score function. Yet, a higher-dimensional embedding space is usually required for a better reasoning capability, which leads to larger model size and hinders applicability to real-world problems (e.g., large-scale KGs or mobile/edge computing). A lightweight modularized KGC solution, called GreenKGC, is proposed in this work to address this issue. GreenKGC consists of three modules: representation learning, feature pruning, and decision learning, to extract discriminant KG features and make accurate predictions on missing relationships using classifiers and negative sampling. Experimental results demonstrate that, in low dimensions, GreenKGC can outperform SOTA methods in most datasets. In addition, low-dimensional GreenKGC can achieve competitive or even better performance against high-dimensional models with a much smaller model size.