Knowledge graph embedding (KGE) aims at learning powerful representations to benefit various artificial intelligence applications. Meanwhile, contrastive learning has been widely leveraged in graph learning as an effective mechanism to enhance the discriminative capacity of the learned representations. However, the complex structures of KG make it hard to construct appropriate contrastive pairs. Only a few attempts have integrated contrastive learning strategies with KGE. But, most of them rely on language models ( e.g., Bert) for contrastive pair construction instead of fully mining information underlying the graph structure, hindering expressive ability. Surprisingly, we find that the entities within a relational symmetrical structure are usually similar and correlated. To this end, we propose a knowledge graph contrastive learning framework based on relation-symmetrical structure, KGE-SymCL, which mines symmetrical structure information in KGs to enhance the discriminative ability of KGE models. Concretely, a plug-and-play approach is proposed by taking entities in the relation-symmetrical positions as positive pairs. Besides, a self-supervised alignment loss is designed to pull together positive pairs. Experimental results on link prediction and entity classification datasets demonstrate that our KGE-SymCL can be easily adopted to various KGE models for performance improvements. Moreover, extensive experiments show that our model could outperform other state-of-the-art baselines.

Negative sequential patterns (NSPs), which capture both frequent occurring and nonoccurring behaviors, become increasingly important and sometimes play a role irreplaceable by analyzing occurring behaviors only. Repetition sequential patterns capture repetitions of patterns in different sequences as well as within a sequence and are very important to understand the repetition relations between behaviors. Though some methods are available for mining NSP and repetition positive sequential patterns (RPSPs), we have not found any methods for mining repetition NSP (RNSP). RNSP can help the analysts to further understand the repetition relationships between items and capture more comprehensive information with repetition properties. However, mining RNSP is much more difficult than mining NSP due to the intrinsic challenges of nonoccurring items. To address the above issues, we first propose a formal definition of repetition negative containment. Then, we propose a method to convert repetition negative containment to repetition positive containment, which fast calculates the repetition supports by only using the corresponding RPSP's information without rescanning databases. Finally, we propose an efficient algorithm, called e-RNSP, to mine RNSP efficiently. To the best of our knowledge, e-RNSP is the first algorithm to efficiently mine RNSP. Intensive experimental results on the first four real and synthetic datasets clearly show that e-RNSP can efficiently discover the repetition negative patterns; results on the fifth dataset prove the effectiveness of RNSP which are captured by the proposed method; and the results on the rest 16 datasets analyze the impacts of data characteristics on mining process.

As an important tool for behavior informatics, negative sequential patterns (NSPs) (such as missing a medical treatment) are sometimes much more informative than positive sequential patterns (PSPs) (e.g., attending a medical treatment) in many applications. However, NSP mining is at an early stage and faces many challenging problems, including 1) how to mine an expected number of NSPs ; 2) how to select useful NSPs ; and 3) how to reduce high time consumption . To solve the first problem, we propose an algorithm Topk-NSP to mine the ${k}$ most frequent negative patterns. In Topk-NSP, we first mine the top- ${k}$ PSPs using the existing methods, and then we use an idea which is similar to top- ${k}$ PSPs mining to mine the top- ${k}$ NSPs from these PSPs. To solve the remaining two problems, we propose three optimization strategies for Topk-NSP. The first optimization strategy is that, in order to consider the influence of PSPs when selecting useful top- ${k}$ NSPs, we introduce two weights, $w_{P}$ and $w_{N}$ , to express the user preference degree for NSPs and PSPs, respectively, and select useful NSPs by a weighted support wsup . The second optimization strategy is to merge wsup and an interestingness metric to select more useful NSPs. The third optimization strategy is to introduce a pruning strategy to reduce the high computational costs of Topk-NSP. Finally, we propose an optimization algorithm Topk-NSP ⁺ . To the best of our knowledge, Topk-NSP ⁺ is the first algorithm that can mine the top- ${k}$ useful NSPs. The experimental results on four synthetic and two real-life data sets show that the Topk-NSP ⁺ is very efficient in mining the top- ${k}$ NSPs in the sense of computational cost and scalability.

Nonoccurring behavior (NOB) studies have attracted the growing attention of scholars as a crucial part of behavioral science. As an effective method to discover both NOB and occurring behaviors (OB), negative sequential pattern (NSP) mining is successfully used in analyzing medical treatment and abnormal behavior patterns. At this time, NSP mining is still an active and challenging research domain. Most of the algorithms are inefficient in practice. Briefly, the key weaknesses of NSP mining are: 1) an inefficient positive sequential pattern (PSP) mining process, 2) a strict constraint of negative containment, and 3) the lack of an effective Negative Sequential Candidate (NSC) generation method. To address these weaknesses, we propose a highly efficient algorithm with improved techniques, named sc-NSP, to mine NSP efficiently. We first propose an improved PrefixSpan algorithm in the PSP mining process, which connects to a bitmap storage structure instead of the original structure. Second, sc-NSP loosens the frequency constraint and exploits the NSC generation method of positive and negative sequential patterns mining (PNSP) (a classic NSP mining method). Furthermore, a novel pruning strategy is designed to reduce the computational complexity of sc-NSP. Finally, sc-NSP obtains the support of NSC by using the most efficient bitwise-based calculation operation. Theoretical analyses show that sc-NSP performs particularly well on data sets with a large number of elements and items in sequence. Comparison and extensive experiments along with case studies on health data show that sc-NSP is 10 times more efficient than other state-of-the-art methods, and the number of NSPs obtained is 5 times greater than other methods.