An unclosed structures-preserving embedding model for signed networks

Signed network embedding has sparked substantial attention since it learns a low-dimensional representation of signed networks. However, most existing methods overestimate the triadic interaction among nodes based on structural balance theory, leaving numerous unclosed structures in a distorted status, which hampers the accurate prediction of future link polarity and exacerbates polarization within networks. To address this issue, we propose the three link statuses preserving embedding model of signed networks, 3LP-SNE, which considers the no-link as a ”special link status” between positive and negative links. Our model captures the structural discrepancies inherent in three link statuses from fundamental binary relations, thereby preserving more complex structures. Specifically, we construct a mapping of three link statuses and distance intervals between nodes combining a three-way decision and a hyperbolic generative model of signed networks. Based on this, the three link statuses preserving is transformed into corresponding distance intervals preserving. Finally, a weighted likelihood function is designed for handling inter-class imbalanced problem and a corresponding optimization algorithm is developed to prevent the maximization of the likelihood function from converging into numerous local optima. The results of the link sign prediction task indicate the value of considering the no-link status and demonstrate the efficacy of our model in preserving primitive structures of signed networks.