DHONE: Density-based Higher-Order Network Embedding

Studies have indicated that focusing solely on pairwise interactions between two nodes disregards the associativity among multi-nodes in the network's local structure. This associativity can be seen as dependencies among nodes, where certain edges' presence depends on the path leading to it. Examinations on diverse datasets have approved that the variable order of chained dependencies allows for the preservation of structure information, which enables the reconstruction of the original network into a Higher-Order Network (HON) with improved quality of network representation. This paper proposes a Density-based Higher-Order Network Embedding (DHONE) algorithm, which integrates the concept of higher-order density into the network-embedding process in order to classify the contribution of different orders of dependencies. Through the construction of a novel and effective higher-order adjacency matrix, DHONE steadily improves the accuracy of network representation learning. Experimental results demonstrate DHONEs proficiency in improving embedding accuracy and overall algorithm robustness. Furthermore, grounded in the concept of higher-order density proposed herein, numerous dependencies have been discerned within the network generated from trajectories, potentially indicating the role of multi-node structures in networks.