# Adap-UIL: A Multi-Feature-Aware User Identity Linkage Framework Based on an Adaptive Graph Walk
## 2 Related Works  
User Identity Linkage, also known as User Alignment, which is the linking of user identities belonging to the same individual in different social networks, is a hot research topic in the field of social networking. It was first introduced by [PERSON] [3] in 2009, and has evolved significantly over the past decade. A recent comprehensive survey by [PERSON] and [PERSON] [2] systematically categorizes existing methods into two core modules: representation generation and alignment learning. This framework highlights the progression of the field from early heuristic approaches to sophisticated machine learning-based solutions. Representation generation methods mainly include traditional methods, optimal transmission-based methods, and embedding-based methods. Traditional methods formulate network alignment as a graph-matching problem, which considers one network as a noisy permutation of the other. These methods directly compute the alignment matrix. IsoRank [4] only applies the structural consistency constraint. BigAlign [5] only leverages attribute consistency. In contrast, REGAL [6] and FINAL [7] incorporate both structural and attribute consistency, employing low-rank matrix approximation to speed up calculations. Optimal transmission-based methods work at the distribution level rather than capturing the neighborhoods of the individual nodes. These methods aim to align graphs by minimizing the cost of transporting one distribution to another. Existing works represent graphs as continuous [8] (e.g., multivariate Gaussian with graph Laplacian covariance) or discrete distributions [9,10] (node-set uniform or statistical feature distributions), minimizing Wasserstein-like discrepancies (e.g., Kullback-Leibler divergence in [10]) for distribution matching. Recent advances integrate position-aware information with Gromov-Wasserstein discrepancy minimization to improve alignment precision, such as FGW [11], using random walk-based cost tensors for hierarchical cluster-node alignment, and PARROT [12], employing random walk regularization on product graphs. Semi-supervised approaches like [13] further optimize the Sinkhorn distance with adaptive entropy regularization, while Galopa [14] innovatively merges optimal transport with graph neural networks for self-supervised learning. Embedding-based methods include three main types, namely, graph neural network-based methods, geometric-based methods, and random walk-based methods. Graph neural network-based methods can excel in Network Alignment (NA) by integrating structural/attribute information but face challenges in capturing higher-order relationships and oversmoothing. Methods like GraphletAlign [15] and SAlign [16] incorporate higher-order structures (graphlets/attention), while GAlign [17] and WAlign [18] concatenate multi-layer embeddings to mitigate oversmoothing. Hypergraph-based GCNs [19] and positional-aware models like NeXtAlign [20] further enrich representations. Geometric-based methods shift to the hyperbolic space rather than Euclidean space, leveraging its efficiency in modeling the hierarchical structures with fewer parameters. HUIL [21] uses the Lorentz model for hyperbolic embedding, while PERFECT [22] employs the Poincare model to unify user-community embeddings but lacks attribute integration. HGENA [23] and HCINA [24] introduce Hyperbolic Graph Convolutional Networks (HGCNs) for attribute-aware embedding, GINA [25] learns dual Euclidean-hyperbolic representations, reconciles them via anchor links, and predicts alignments by merging intranetwork embeddings. Random walk-based methods have advanced significantly, yet they commonly suffer from undifferentiated node traversal. PALE [26] and Deeplink [27] rely on generic random walks that treat all neighborhood nodes equally, neglecting structural hierarchy. FRUI-P [28] and CENA [29] use walk-based context modeling, but CENA's \(\alpha\) jumping probability applies uniformly across nodes rather than adapting to local features.