Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more 'compatible', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices between two graphs is computed. A significant portion of the literature on this problem only takes the global structure of the input graphs into account. Only more recent ones additionally use vertex and edge attributes to achieve a more accurate alignment. However, these methods are not designed to scale to map large graphs arising in many modern applications. We propose a new iterative graph aligner, gsaNA, that uses the global structure of the graphs to significantly reduce the problem size and align large graphs with a minimal loss of information. Concretely, we show that our proposed technique is highly flexible, can be used to achieve higher recall, and it is orders of magnitudes faster than the current state of the art techniques.
@cite_31: 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.
@cite_18: We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The algorithm allows to analyze large graphs and may find applications in fields such as computational biology. As a proof of concept we use our algorithm to align the similarity graphs of two interacting protein families involved in bacterial signal transduction, and to predict actually interacting protein partners between these families.
@cite_8: 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.
NetAlign @cite_31 formulates the network alignment problem as an integer quadratic programming problem to maximize the number of squares''. A near-optimal solution is obtained by finding the maximum a posteriori assignment using belief propagation heuristic and message-passing algorithms which yield near optimal results in practice. Another message passing network alignment algorithm on top of belief propagation is proposed by @cite_18 . @cite_8 propose to align two bipartite graphs with a fast projected gradient descent algorithm which exploits the structural properties of the graphs.