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.
Solution methods proposed in the literature for graph alignment can be roughly classified into four basic categories @cite_4 @cite_1 : spectral methods @cite_16 @cite_17 @cite_27 @cite_7 , graph structure similarity methods @cite_36 @cite_32 @cite_19 @cite_13 @cite_20 , tree search or tabu search methods @cite_34 @cite_14 @cite_10 @cite_3 , and integer linear programming (ILP) methods @cite_22 @cite_9 @cite_31 . All of these works have scalability issues. Our algorithms leverage global graph structure and reduces the problem space and augment that with semantic information to alleviate most of the scalability issues.
@cite_14 @cite_4 @cite_22 @cite_7 @cite_36 @cite_10 @cite_9 @cite_1 @cite_32 @cite_34 @cite_3 @cite_19 @cite_27 @cite_31 @cite_16 @cite_13 @cite_20 @cite_17
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The growing popularity of graph databases has generated interesting data management problems, such as subgraph search, shortest-path query, reachability verification, and pattern match. Among these, a pattern match query is more flexible compared to a subgraph search and more informative compared to a shortest-path or reachability query. In this paper, we address pattern match problems over a large data graph G. Specifically, given a pattern graph (i.e., query Q), we want to find all matches (in G) that have the similar connections as those in Q. In order to reduce the search space significantly, we first transform the vertices into points in a vector space via graph embedding techniques, coverting a pattern match query into a distance-based multi-way join problem over the converted vector space. We also propose several pruning strategies and a join order selection method to process join processing efficiently. Extensive experiments on both real and synthetic datasets show that our method outperforms existing ones by orders of magnitude. In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection. Due to its wide range of applications, matching between two graphs has been extensively studied and remains an active topic. By contrast, it is still under-exploited on how to jointly match multiple graphs, partly due to its intrinsic combinatorial intractability. In this work, we address this challenging problem in a principled way under the rank-1 tensor approximation framework. In particular, we formulate multi-graph matching as a combinational optimization problem with two main ingredients: unary matching over graph vertices and structure matching over graph edges, both of which across multiple graphs. Then we propose an efficient power iteration solution for the resulting NP-hard optimization problem. The proposed algorithm has several advantages: 1) the intrinsic matching consistency across multiple graphs based on the high-order tensor optimization, 2) the free employment of powerful high-order node affinity, 3) the flexible integration between various types of node affinities and edge hyper-edge affinities. Experiments on diverse and challenging datasets validate the effectiveness of the proposed approach in comparison with state-of the-arts. 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.