# Heterogeneous Graph Structure Learning for Next Point-of-Interest Recommendation
## 2 Literature Review
### Graph Structure Learning  
Although graph neural networks have achieved significant success in addressing graph-related problems, many models still use artificially defined graphs that may contain noise or missing edges. This can degrade the quality of the representation vectors and, in the end, affect the performance of downstream tasks. To address the uncertainties in graphs,some models are proposed to use graph structure learning to learn an optimal graph structure during training process. Graph structure learning research can be broadly categorized into three types: metric learning, probabilistic modeling, and direct optimization.  
Models based on metric learning calculate the similarity between nodes by their representation vectors, thereby updating the probability of edges existing between nodes. For example, IDGL [40] alternates between learning the graph structure and the representation vectors, assuming that a good graph structure can generate a good representation vector, and vice versa. AGCN [41] learns a task-oriented adaptive graph structure for each graph dataset during training, using distance metric learning to learn the graph structure. AM-GCN [42] extracts embeddings from node features, the graph's topological structure, and their combinations, and uses an attention mechanism to learn weights.  
The model based on probabilistic modeling learns a probability distribution related to the edges from the graph, and then samples a graph from this distribution. For example, LDS [43] learns the discrete probability distribution of the graphs edges by solving a two-layer program that combines the graph structure and GCN parameters, and then samples the graph structure from this distribution. PTDNet [44] enhances the robustness and generalization of GNNs by discarding edges irrelevant to the task. NeuralSparse [45] uses both structural and non-structural information as inputs, employing neural networks to sparsify the graph structure and remove edges that may be irrelevant to the task.  
The direct optimization model treats the adjacency matrix of the graph as parameters, optimizing it alongside other GNN parameters. For example, GLNN [46] optimizes the graph directly using data and tasks. ProGNN [47] leverages the unique properties of the graph to optimize both its structure and GNN parameters, aiming to simultaneously learn better graph structures and GNN models from the perturbed graph. TO-GCN [48] uses labels to optimize the parameters of the adjacency matrix and to learn the GNN parameters. GGEN [49] addresses the challenges of missing or disconnected graph structures in the real world and employ a multi-branch generation structure to obtain diverse graph topologies. BiGSL [50] considers the hierarchical relations among POIs and the graphs often suffer from noise or incompleteness. A hierarchical graph is iteratively learned to refine the graph structures. Additionally, it employs a contrastive multiview fusion to increase the recommendation performance. RGSL [51] considers the challenge in heterophilic graphs, where connected nodes may have different labels. It uses a filter to enhance node distinctiveness and a contrastive regularizer to refine the graph's structure.