One of the major challenges in applications related to social networks, computational biology, collaboration networks etc., is to efficiently search for similar patterns in their underlying graphs. These graphs are typically noisy and contain thousands of vertices and millions of edges. In many cases, the graphs are unlabelled and the notion of similarity is also not well defined. We study the problem of searching an induced sub graph in a large target graph that is most similar to the given query graph. We assume that the query graph and target graph are undirected and unlabelled. We use graph let kernels [1] to define graph similarity. Graph let kernels are known to perform better than other kernels in different applications.
Similarity based graph searching has been studied in the past under various settings. In many of the previous works, it is assumed that the graphs are labeled. In one class of problems, a large database of graphs is given and the goal is to find the most similar match in the database with respect to the given query graph @cite_0 @cite_8 @cite_27 @cite_2 @cite_30 @cite_12 . In the second class, given a target graph and a query graph, subgraph of the target graph that is most similar to the query graph needs to be identified @cite_19 @cite_16 @cite_7 @cite_33 . Different notions of similarity were also explored in the past for these classes of problems.
@cite_30 @cite_33 @cite_7 @cite_8 @cite_0 @cite_19 @cite_27 @cite_2 @cite_16 @cite_12
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Due to many real applications of graph databases, it has become increasingly important to retrieve graphs g (in graph database D) that approximately match with query graph q, rather than exact subgraph matches. In this paper, we study the problem of graph similarity search, which retrieves graphs that are similar to a given query graph under the constraint of the minimum edit distance. Specifically, we derive a lower bound, branch-based bound, which can greatly reduce the search space of the graph similarity search. We also propose a tree index structure, namely b-tree, to facilitate effective pruning and efficient query processing. Extensive experiments confirm that our proposed approach outperforms the existing approaches by orders of magnitude, in terms of both pruning power and query response time. 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. The growing popularity of graph databases has generated interesting data management problems, such as subgraph search, shortest path query, reachability verification, and pattern matching. Among these, a pattern match query is more flexible compared with a subgraph search and more informative compared with a shortest path or a reachability query. In this paper, we address distance-based pattern match queries over a large data graph G. Due to the huge search space, we adopt a filter-and-refine framework to answer a pattern match query over a large graph. We first find a set of candidate matches by a graph embedding technique and then evaluate these to find the exact matches. Extensive experiments confirm the superiority of our method.