Disease-related association prediction is a crucial task in the biomedical field, aiming to identify relations between diseases and various biological entities such as RNAs (like circRNAs, lncRNAs), drugs and genes. Understanding these interactions not only deepens our understanding of pathological mechanisms, but also facilitates the development of novel diagnostic tools, therapeutic strategies, and preventive measures. Current challenges in disease-related association prediction primarily encompass data sparsity, data heterogeneity, limited generalization ability, and the absence of a unified analytical framework. To address the above issues, we propose a hybrid framework integrating dynamics mechanisms and graph convolutional networks in hyperbolic space for disease-related association prediction. Our approach begins by constructing a heterogeneous network using interaction information to represent multiple types of biological associations. This network is then processed through a game-guided dynamics mechanism that incorporates both individual node features and other influences. The hyperbolic graph convolutional network is then designed to model hierarchical and scale-free graph-structured data. Comprehensive experimental results on multiple types of associations demonstrate that our model achieves high predictive performance. The results of the case study validate the robust predictive capability of our proposed method in the prediction of disease-related associations.

Hyperedges, as extensions of pairwise edges, can characterize higher-order relations among multiple individuals. Due to the necessity of hypergraph detection in practical systems, hyperedge prediction has become a frontier problem in complex networks. However, previous hyperedge prediction models encounter three challenges: (i) failing to predict dynamic and arbitrary-order hyperedges simultaneously, (ii) confusing higher-order and lower-order features together to propagate neighborhood information, and (iii) lacking the capability to learn physical evolution laws, which lead to poor performance of the models. To tackle these challenges, we propose D$^{3}$HP, aDual-viewDesynchronization hypergraph learning for arbitrary-orderDynamicHyperedgePrediction. Specifically, D$^{3}$HP extracts the dynamic higher-order and lower-order features of hyperedges separately through an elastic hypergraph neural network (EHGNN) and an alternate desynchronization graph convolutional network (ADGCN) at each time snapshot. EHGNN is designed to incrementally mine the implicit higher-order relations and propagate neighborhood information. Moreover, ADGCN aims to combine GCN with desynchronization learining to learn the physical evolution of lower-order relations and alleviate the over-smoothing problem. Further, we improve the prediction performance of the model by rationally fusing the features learned from the dual views. Extensive experiments on 8 dynamic higher-order networks demonstrate that D$^{3}$HP outperforms 14 state-of-the-art baselines.

Recently, higher order patterns have played an important role in network structure analysis. The simplices in higher order patterns enrich dynamic network modeling and provide strong structural feature information for feature learning. However, the disorder dynamic network with simplex patterns has not been organized and divided according to time windows. Besides, existing methods do not make full use of the feature information to predict the simplex patterns with higher orders. To address these issues, we propose a simplex pattern prediction method based on dynamic higher order path convolutional networks. First, we divide the dynamic higher order datasets into different network structures under continuous-time windows, which possess complete time information. Second, feature extraction is performed on the network structure of continuous-time windows through higher order path convolutional networks. Subsequently, we embed time nodes into feature encoding and obtain feature representations of simplex patterns through feature fusion. The obtained feature representations of simplices are recognized by a simplex pattern discriminator to predict the simplex patterns at different moments. Finally, compared to other dynamic graph representation learning algorithms, our proposed algorithm has significantly improved its performance in predicting simplex patterns on five real dynamic higher order datasets.