Semi-supervised learning (SSL) offers a robust framework for harnessing the potential of unannotated data. Traditionally, SSL mandates that all classes possess labeled instances. However, the emergence of open-world SSL (OwSSL) introduces a more practical challenge, wherein unlabeled data may encompass samples from unseen classes. This scenario leads to misclassification of unseen classes as known ones, consequently undermining classification accuracy. To overcome this challenge, this study revisits two methodologies from self-supervised and semi-supervised learning, self-labeling and consistency, tailoring them to address the OwSSL problem. Specifically, we propose an effective framework called _OwMatch_, combining conditional self-labeling and open-world hierarchical thresholding. Theoretically, we analyze the estimation of class distribution on unlabeled data through rigorous statistical analysis, thus demonstrating that OwMatch can ensure the unbiasedness of the label assignment estimator with reliability. Comprehensive empirical analyses demonstrate that our method yields substantial performance enhancements across both known and unknown classes in comparison to previous studies. Code is available at [https://github.com/niusj03/OwMatch](https://github.com/niusj03/OwMatch).

In order to meet the problems caused by sparse data and computational efficiency, knowledge graph (KG) is adopted to represent the semantic information of entities and relations as dense and low-dimensional vectors. While conventional KG representation methods mainly focuse on static data. These methods fail to deal with data that evolves with time which may only be valid for a certain period of time. To accommodate this problem, a temporal KG embedding model based on tensor decomposition is proposed in this paper, which regards the fact set in the KG as a fourth-order tensor including head entities, relations, tail entities and time dimensions. This method can be further generalized to other static KG embedding based on tensor decomposition. With experiments on temporal datasets extracted from real-world KG, extensive experiment results show that our approach outperforms state-of-the-art methods of KG embedding.