How can we efficiently and accurately factorize multi-source data in dynamic and real-time environments? Coupled matrix-tensor factorization (CMTF) is a powerful tool for such tasks, but existing methods often struggle with scalability, particularly when dealing with continuously streaming data. Traditional CMTF approaches, while effective at capturing complex relationships, suffer from computational inefficiencies and the need for retraining as new data arrive. Moreover, many techniques fail to properly incorporate the inherent temporal characteristics of the data, which could significantly enhance both accuracy and convergence speed.

How can we accurately recognize overlapping entity spans in text while effectively capturing global context among spans? Nested Named Entity Recognition (nested NER) becomes challenging in the presence of nested or overlapping entity spans. Traditional span-based methods enumerate all possible spans, resulting in high computational costs and severe label imbalance from excessive negative spans which are non-entities. Additionally, they often fail to fully capture global context among overlapping entities.

How can we accurately decompose a temporal irregular tensor along with a related knowledge graph tensor? The PARAFAC2 decomposition is widely used for analyzing irregular tensors composed of matrices with varying row sizes. Recent advancements in PARAFAC2 methods primarily focus on capturing dynamic features that change over time, since data irregularities often arise from temporal fluctuations. However, these methods often neglect static features, such as knowledge information, which remain constant over time.In this paper, we propose KG-CTF (Knowledge Graph-based Coupled Tensor Factorization), a coupled tensor factorization method designed to capture both dynamic and static features within an irregular tensor. To incorporate knowledge graph tensors as static features, KG-CTF couples an irregular temporal tensor with a knowledge graph tensor that share a common axis. Additionally, KG-CTF employs a relational regularization to capture relationships among the factor matrices of the knowledge graph tensor. For accelerated convergence of the factor matrices, KG-CTF utilizes momentum update techniques. Extensive experiments show that KG-CTF reduces error rates by up to 1.64× compared to existing PARAFAC2 methods.

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