Knowledge Graph (KG) reasoning that predicts missing facts for incomplete KGs has been widely explored. However, reasoning over Temporal KG (TKG) that predicts facts in the future is still far from resolved. The key to predict future facts is to thoroughly understand the historical facts. A TKG is actually a sequence of KGs corresponding to different timestamps, where all concurrent facts in each KG exhibit structural dependencies and temporally adjacent facts carry informative sequential patterns. To capture these properties effectively and efficiently, we propose a novel Recurrent Evolution network based on Graph Convolution Network (GCN), called RE-GCN, which learns the evolutional representations of entities and relations at each timestamp by modeling the KG sequence recurrently. Specifically, for the evolution unit, a relation-aware GCN is leveraged to capture the structural dependencies within the KG at each timestamp. In order to capture the sequential patterns of all facts in parallel, the historical KG sequence is modeled auto-regressively by the gate recurrent components. Moreover, the static properties of entities such as entity types, are also incorporated via a static graph constraint component to obtain better entity representations. Fact prediction at future timestamps can then be realized based on the evolutional entity and relation representations. Extensive experiments demonstrate that the RE-GCN model obtains substantial performance and efficiency improvement for the temporal reasoning tasks on six benchmark datasets. Especially, it achieves up to 11.46\% improvement in MRR for entity prediction with up to 82 times speedup comparing to the state-of-the-art baseline.

Knowledge graph embedding aims to represent entities and relations in a large-scale knowledge graph as elements in a continuous vector space. Existing methods, e.g., TransE and TransH, learn embedding representation by defining a global margin-based loss function over the data. However, the optimal loss function is determined during experiments whose parameters are examined among a closed set of candidates. Moreover, embeddings over two knowledge graphs with different entities and relations share the same set of candidate loss functions, ignoring the locality of both graphs. This leads to the limited performance of embedding related applications. In this paper, we propose a locally adaptive translation method for knowledge graph embedding, called TransA, to find the optimal loss function by adaptively determining its margin over different knowledge graphs. Experiments on two benchmark data sets demonstrate the superiority of the proposed method, as compared to the-state-of-the-art ones.

As an important tool for information filtering in the era of socialized web, recommender systems have witnessed rapid development in the last decade. As benefited from the better interpretability, neighborhood-based collaborative filtering techniques, such as item-based collaborative filtering adopted by Amazon, have gained a great success in many practical recommender systems. However, the neighborhood-based collaborative filtering method suffers from the rating bound problem, i.e., the rating on a target item that this method estimates is bounded by the observed ratings of its all neighboring items. Therefore, it cannot accurately estimate the unobserved rating on a target item, if its ground truth rating is actually higher (lower) than the highest (lowest) rating over all items in its neighborhood. In this paper, we address this problem by formalizing rating estimation as a task of recovering a scalar rating function. With a linearity assumption, we infer all the ratings by optimizing the low-order norm, e.g., the $l_1/2$-norm, of the second derivative of the target scalar function, while remaining its observed ratings unchanged. Experimental results on three real datasets, namely Douban, Goodreads and MovieLens, demonstrate that the proposed approach can well overcome the rating bound problem. Particularly, it can significantly improve the accuracy of rating estimation by 37% than the conventional neighborhood-based methods.