Multi-relational networks play an important role in today's world and are utilized to capture complex relationships between the data. Their applications span many domains such as biomedical, financial, social, etc., and because of their increasing usability, it becomes crucial to find efficient ways to deal with the added complexity of multiple layers. In this work, we propose a novel approach to represent these complex networks using a single aggregated adjacency matrix, by utilizing primes as surrogates for the relations. Due to the fundamental theorem of arithmetic, this allows for a lossless, compact representation of the whole multi-relational graph, using a single adjacency matrix. Moreover, this representation enables the fast computation of multi-hop adjacency matrices, that can be useful for a variety of downstream tasks. We present simple and complex tasks in which this representation can be useful and showcase its efficiency and performance. Finally, we also provide insights on the advantages and the open challenges that still need to be addressed and motivate future work.
翻译:多关系网络在当今世界中起着重要作用,并被用来捕捉数据之间的复杂关系。它们的应用涉及生物医学、金融、社会等许多领域,而且由于它们越来越有用,因此找到有效方法处理复杂多层次的复杂问题变得至关重要。在这项工作中,我们提出一种新颖的办法,利用一个单一的组合组合式的对等关系矩阵来代表这些复杂网络,利用黄金作为关系代位。由于算术的基本理论,这允许利用单一的对等矩阵来代表整个多关系图的无损、紧凑的表述。此外,这种表述使得能够快速计算多希望对下游任务有用的多希望对等矩阵。我们提出了简单而复杂的任务,在其中这种表述可以有用,并展示其效率和业绩。最后,我们还就仍然需要解决的优势和公开挑战提供了见解。