You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Graph alignment, also known as network alignment, is a fundamental task in social network analysis. Many recent works have relied on partially labeled cross-graph node correspondences, i.e., anchor links. However, due to the privacy and security issue, the manual labeling of anchor links for diverse scenarios may be prohibitive. Aligning two graphs without any anchor links is a crucial and challenging task. In this paper, we propose an Unsupervised Adversarial Graph Alignment (UAGA) framework to learn a cross-graph alignment between two embedding spaces of different graphs in a fully unsupervised fashion ( no existing anchor links and no users' personal profile or attribute information is available). The proposed framework learns the embedding spaces of each graph, and then attempts to align the two spaces via adversarial training, followed by a refinement procedure. We further extend our UAGA method to incremental UAGA (iUAGA) that iteratively reveals the unobserved user links based on the pseudo anchor links. This can be used to further improve both the embedding quality and the alignment accuracy. Moreover, the proposed methods will benefit some real-world applications, link prediction in social networks. Comprehensive experiments on real-world data demonstrate the effectiveness of our proposed approaches UAGA and iUAGA for unsupervised graph alignment.

Cited Abstract(s):
[1]: Background: In addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NPhard problems. Most previous algorithmic work on network alignments is heuristic in nature. Results: We introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem. Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and – unlike those computed by pure heuristics – come with a quality guarantee. Conclusion: Computational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LISA library.

[2]: Protein–protein interactions (PPIs) and their networks play a central role in all biological processes. Akin to the complete sequencing of genomes and their comparative analysis, complete descriptions of interactomes and their comparative analysis is fundamental to a deeper understanding of biological processes. A first step in such an analysis is to align two or more PPI networks. Here, we introduce an algorithm, IsoRank, for global alignment of multiple PPI networks. The guiding intuition here is that a protein in one PPI network is a good match for a protein in another network if their respective sequences and neighborhood topologies are a good match. We encode this intuition as an eigenvalue problem in a manner analogous to Google's PageRank method. Using IsoRank, we compute a global alignment of the Saccharomyces cerevisiae, Drosophila melanogaster, Caenorhabditis elegans, Mus musculus, and Homo sapiens PPI networks. We demonstrate that incorporating PPI data in ortholog prediction results in improvements over existing sequence-only approaches and over predictions from local alignments of the yeast and fly networks. Previous methods have been effective at identifying conserved, localized network patterns across pairs of networks. This work takes the further step of performing a global alignment of multiple PPI networks. It simultaneously uses sequence similarity and network data and, unlike previous approaches, explicitly models the tradeoff inherent in combining them. We expect IsoRank—with its simultaneous handling of node similarity and network similarity—to be applicable across many scientific domains.

[3]: We propose a new distributed algorithm for sparse variants of the network alignment problem, which occurs in a variety of data mining areas including systems biology, database matching, and computer vision. Our algorithm uses a belief propagation heuristic and provides near optimal solutions for this NP-hard combinatorial optimization problem. We show that our algorithm is faster and outperforms or ties existing algorithms on synthetic problems, a problem in bioinformatics, and a problem in ontology matching. We also provide a unified framework for studying and comparing all network alignment solvers.

[4]: How can we find the virtual twin (i.e., the same or similar user) on Linked In for a user on Facebook? How can we effectively link an information network with a social network to support cross-network search? Graph alignment - the task of finding the node correspondences between two given graphs - is a fundamental building block in numerous application domains, such as social networks analysis, bioinformatics, chemistry, pattern recognition. In this work, we focus on aligning bipartite graphs, a problem which has been largely ignored by the extensive existing work on graph matching, despite the ubiquity of those graphs (e.g., users-groups network). We introduce a new optimization formulation and propose an effective and fast algorithm to solve it. We also propose a fast generalization of our approach to align unipartite graphs. The extensive experimental evaluations show that our method outperforms the state-of-art graph matching algorithms in both alignment accuracy and running time, being up to 10x more accurate or 174x faster on real graphs.
The graph alignment, which aims to find node correspondence across different graphs, has attracted lots of research interests with extensive literatures in the past decade. Graph alignment was first studied by exploring the graph structure to align the topology of the underlying graphs. For example, IsoRank [2] aligns different graphs greedily based on the pairwise topology similarities ( node similarity) calculated with spectral graph theory and finds the alignment by solving the maximum bipartite matching. NetAlign [3] proposes a distributed and efficient algorithm for the sparse bipartite graph matching problem by using the max-product belief propagation based on the graph topology. UniAlign [4] proposes to distinguish the nodes of graphs by types ( users and groups) and find the correspondences at different granularities at once for the fast bipartite or unipartite graph matching problem. Klau [1] formulates the pairwise global graph alignment problem as the graph-based maximum structural matching problem, which is solved by a Lagrangian relaxation approach. These approaches, however, ignore the rich attribute information on nodes and or edges in many real graphs and are prone to lead to sub-optimal results.