Hyper-relational knowledge graphs (HKGs) extend the traditional triplet-based knowledge graph by adding qualifiers to the relationships, making HKGs particularly useful for tasks that require more profound understanding and inference from relationships between entities. However, existing hyper-relational knowledge representation learning methods (HKRL) focus on direct neighbourhood information of entities only by neglecting the relational similarity of the main triple in hyper-relational facts and the attribute details in the qualifiers. In addition, few works extract common and private information across multiple views to minimize noise and interference. This paper proposes a multi-hypergraph disentanglement method for HKRL to address the above issues. Specifically, we first construct four hypergraphs to mine and utilise the inherent structure information of HKGs, and then propose to extract common representations among hypergraphs and private representations within individual hypergraphs to mine the semantic information and the task-relevant information, respectively. Experiment results on four real datasets demonstrate the effectiveness of the proposed method compared to SOTA methods in link prediction tasks on HKGs.

It has been demonstrated that the segmentation performance is highly dependent on both subspace preservation and graph connectivity. In the literature, the full connectivity method linearly represents each data point ( e.g., a pixel in one image) by all data points for achieving subspace preservation, while the sparse connectivity method was designed to linearly represent each data point by a set of data points for achieving graph connectivity. However, previous methods only focused on either subspace preservation or graph connectivity. In this article, we propose a Sparse Graph Connectivity (SGC) method for image segmentation to automatically learn the affinity matrix from the low-dimensional space of original data, which aims at simultaneously achieving subspace preservation and graph connectivity. To do this, the proposed SGC simultaneously learns a self-representation affinity matrix for subspace preservation and a sparse affinity matrix for graph connectivity, from the intrinsic low-dimensional feature space of high-dimensional original data. Meanwhile, the self-representation affinity matrix is pushed to be similar to the sparse affinity as well as be the final segmentation results. Experimental result on synthetic and real-image datasets showed that our SGC method achieved the best segmentation performance, compared to state-of-the-art segmentation methods.