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_22: 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.
@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.
@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_16: We describe an algorithm, IsoRank, for global alignment of two protein-protein interaction (PPI) networks. IsoRank aims to maximize the overall match between the two networks; in contrast, much of previous work has focused on the local alignment problem-- identifying many possible alignments, each corresponding to a local region of similarity. IsoRank is guided by the intuition that a protein should be matched with a protein in the other network if and only if the neighbors of the two proteins can also be well matched. We encode this intuition as an eigenvalue problem, in a manner analogous to Google's PageRank method. We use IsoRank to compute the first known global alignment between the S. cerevisiae and D. melanogaster PPI networks. The common subgraph has 1420 edges and describes conserved functional components between the two species. Comparisons of our results with those of a well-known algorithm for local network alignment indicate that the globally optimized alignment resolves ambiguity introduced by multiple local alignments. Finally, we interpret the results of global alignment to identify functional orthologs between yeast and fly; our functional ortholog prediction method is much simpler than a recently proposed approach and yet provides results that are more comprehensive.
@cite_12: Multiple networks naturally appear in numerous high-impact applications. Network alignment (i.e., finding the node correspondence across different networks) is often the very first step for many data mining tasks. Most, if not all, of the existing alignment methods are solely based on the topology of the underlying networks. Nonetheless, many real networks often have rich attribute information on nodes and or edges. In this paper, we propose a family of algorithms FINAL to align attributed networks. The key idea is to leverage the node edge attribute information to guide (topology-based) alignment process. We formulate this problem from an optimization perspective based on the alignment consistency principle, and develop effective and scalable algorithms to solve it. Our experiments on real networks show that (1) by leveraging the attribute information, our algorithms can significantly improve the alignment accuracy (i.e., up to a 30 improvement over the existing methods); (2) compared with the exact solution, our proposed fast alignment algorithm leads to a more than 10 times speed-up, while preserving a 95 accuracy; and (3) our on-query alignment method scales linearly, with an around 90 ranking accuracy compared with our exact full alignment method and a near real-time response time.
In a more recent work, propose Final @cite_12 to solve attributed network alignment problem. Final extends the concept of IsoRank @cite_16 , and make it capable to benefit from attribute information of the vertices and edges to solve this problem. In addition to graph's vertex, edge and attribute sets Final adds an optional input called prior knowledge matrix (H) in which each entry gives likelihood to align two vertices. Final is one of the most recent works which solves attributed graph alignment problem and outperforms @cite_16 @cite_22 @cite_31 @cite_8 .