  Link prediction has been widely studied as an important research direction.
Higher-order link prediction has gained especially significant attention since
higher-order networks provide a more accurate description of real-world complex
systems. However, higher-order networks contain more complex information than
traditional pairwise networks, making the prediction of higher-order links a
formidable challenging task. Recently, researchers have discovered that local
features have advantages over long-range features in higher-order link
prediction. Therefore, it is necessary to develop more efficient and concise
higher-order link prediction algorithms based on local features. In this paper,
we proposed two similarity metrics via local information, simplicial
decomposition weight (SDW) and closed ratio weight (CRW), to predict possible
future higher-order interactions (simplices) in simplicial networks. These two
algorithms capture local higher-order information at two aspects: simplex
decomposition and cliques' state (closed or open). We tested their performance
in eight empirical simplicial networks, and the results show that our proposed
metrics outperform other benchmarks in predicting third-order and fourth-order
interactions (simplices) in most cases. In addition, we explore the robustness
of the proposed algorithms, and the results suggest that the performance of
these novel algorithms is advanced under different sizes of training sets.
