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165
Graph Indexing: A Frequent Structurebased Approach
, 2004
"... Graph has become increasingly important in modelling complicated structures and schemaless data such as proteins, chemical compounds, and XML documents. Given a graph query, it is desirable to retrieve graphs quickly from a large database via graphbased indices. In this paper, we investigate the is ..."
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Cited by 201 (25 self)
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Graph has become increasingly important in modelling complicated structures and schemaless data such as proteins, chemical compounds, and XML documents. Given a graph query, it is desirable to retrieve graphs quickly from a large database via graphbased indices. In this paper, we investigate the issues of indexing graphs and propose a novel solution by applying a graph mining technique. Di#erent from the existing pathbased methods, our approach, called gIndex, makes use of frequent substructure as the basic indexing feature. Frequent substructures are ideal candidates since they explore the intrinsic characteristics of the data and are relatively stable to database updates. To reduce the size of index structure, two techniques, sizeincreasing support constraint and discriminative fragments, are introduced. Our performance study shows that gIndex has 10 times smaller index size, but achieves 310 times better performance in comparison with a typical pathbased method, GraphGrep. The gIndex approach not only provides an elegant solution to the graph indexing problem, but also demonstrates how database indexing and query processing can benefit from data mining, especially frequent pattern mining. Furthermore, the concepts developed here can be applied to indexing sequences, trees, and other complicated structures as well.
Efficient Mining of Frequent Subgraph in the Presence of Isomorphism
"... Frequent subgraph mining is an active research topic in the data mining community. A graph is a general model to represent data and has been used in many domains like cheminformatics and bioinformatics. Mining patterns from graph databases is challenging since graph related operations, such as subgr ..."
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Cited by 194 (23 self)
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Frequent subgraph mining is an active research topic in the data mining community. A graph is a general model to represent data and has been used in many domains like cheminformatics and bioinformatics. Mining patterns from graph databases is challenging since graph related operations, such as subgraph testing, generally have higher time complexity than the corresponding operations on itemsets, sequences, and trees, which have been studied extensively. In this paper, we propose a novel frequent subgraph mining algorithm: FFSM, which employs a vertical search scheme within an algebraic graphical framework we have developed to reduce the number of redundant candidates proposed. Our empirical study on synthetic and real datasets demonstrates that FFSM achieves a substantial performance gain over the current startoftheart subgraph mining algorithm gSpan.
Frequent SubStructureBased Approaches for Classifying Chemical Compounds
 In Proceedings of ICDM’03
, 2003
"... In this paper we study the problem of classifying chemical compound datasets. We present a substructurebased classification algorithm that decouples the substructure discovery process from the classification model construction and uses frequent subgraph discovery algorithms to find all topologi ..."
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Cited by 140 (6 self)
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In this paper we study the problem of classifying chemical compound datasets. We present a substructurebased classification algorithm that decouples the substructure discovery process from the classification model construction and uses frequent subgraph discovery algorithms to find all topological and geometric substructures present in the dataset. The advantage of our approach is that during classification model construction, all relevant substructures are available allowing the classifier to intelligently select the most discriminating ones. The computational scalability is ensured by the use of highly efficient frequent subgraph discovery algorithms coupled with aggressive feature selection. Our experimental evaluation on eight different classification problems shows that our approach is computationally scalable and outperforms existing schemes by 10% to 35%, on the average.
Finding frequent patterns in a large sparse graph
 SIAM Data Mining Conference
, 2004
"... This paper presents two algorithms based on the horizontal and vertical pattern discovery paradigms that find the connected subgraphs that have a sufficient number of edgedisjoint embeddings in a single large undirected labeled sparse graph. These algorithms use three different methods to determine ..."
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Cited by 130 (4 self)
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This paper presents two algorithms based on the horizontal and vertical pattern discovery paradigms that find the connected subgraphs that have a sufficient number of edgedisjoint embeddings in a single large undirected labeled sparse graph. These algorithms use three different methods to determine the number of the edgedisjoint embeddings of a subgraph that are based on approximate and exact maximum independent set computations and use it to prune infrequent subgraphs. Experimental evaluation on real datasets from various domains show that both algorithms achieve good performance, scale well to sparse input graphs with more than 100,000 vertices, and significantly outperform a previously developed algorithm.
An efficient algorithm for discovering frequent subgraphs
 IEEE Transactions on Knowledge and Data Engineering
, 2002
"... Abstract — Over the years, frequent itemset discovery algorithms have been used to find interesting patterns in various application areas. However, as data mining techniques are being increasingly applied to nontraditional domains, existing frequent pattern discovery approach cannot be used. This i ..."
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Cited by 120 (7 self)
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Abstract — Over the years, frequent itemset discovery algorithms have been used to find interesting patterns in various application areas. However, as data mining techniques are being increasingly applied to nontraditional domains, existing frequent pattern discovery approach cannot be used. This is because the transaction framework that is assumed by these algorithms cannot be used to effectively model the datasets in these domains. An alternate way of modeling the objects in these datasets is to represent them using graphs. Within that model, one way of formulating the frequent pattern discovery problem is as that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a computationally efficient algorithm, called FSG, for finding all frequent subgraphs in large graph datasets. We experimentally evaluate the performance of FSG using a variety of real and synthetic datasets. Our results show that despite the underlying complexity associated with frequent subgraph discovery, FSG is effective in finding all frequently occurring subgraphs in datasets containing over 200,000 graph transactions and scales linearly with respect to the size of the dataset. Index Terms — Data mining, scientific datasets, frequent pattern discovery, chemical compound datasets.
Spin: Mining maximal frequent subgraphs from graph databases
 IN KDD
, 2004
"... One fundamental challenge for mining recurring subgraphs from semistructured data sets is the overwhelming abundance of such patterns. In large graph databases, the total number of frequent subgraphs can become too large to allow a full enumeration using reasonable computational resources. In this ..."
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Cited by 99 (12 self)
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One fundamental challenge for mining recurring subgraphs from semistructured data sets is the overwhelming abundance of such patterns. In large graph databases, the total number of frequent subgraphs can become too large to allow a full enumeration using reasonable computational resources. In this paper, we propose a new algorithm that mines only maximal frequent subgraphs, i.e. subgraphs that are not a part of any other frequent subgraphs. This may exponentially decrease the size of the output set in the best case; in our experiments on practical data sets, mining maximal frequent subgraphs reduces the total number of mined patterns by two to three orders of magnitude. Our method first mines all frequent trees from a general graph database and then reconstructs all maximal subgraphs from the mined trees. Using two chemical structure benchmarks and a set of synthetic graph data sets, we demonstrate that, in addition to decreasing the output size, our algorithm can achieve a fivefold speed up over the current stateoftheart subgraph mining algorithms.
Cyclic pattern kernels for Predictive graph mining
, 2004
"... With applications in biology, the worldwide web, and several other areas, mining of graphstructured objects has received significant interest recently. One of the major research directions in this field is concerned with predictive data mining in graph databases where each instance is represented ..."
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Cited by 73 (2 self)
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With applications in biology, the worldwide web, and several other areas, mining of graphstructured objects has received significant interest recently. One of the major research directions in this field is concerned with predictive data mining in graph databases where each instance is represented by a graph. Some of the proposed approaches for this task rely on the excellent classification performance of support vector machines. To control the computational cost of these approaches, the underlying kernel functions are based on frequent patterns. In contrast to these approaches, we propose a kernel function based on a natural set of cyclic and tree patterns independent of their frequency, and discuss its computational aspects. To practically demonstrate the effectiveness of our approach, we use the popular NCIHIV molecule dataset. Our experimental results show that cyclic pattern kernels can be computed quickly and offer predictive performance superior to recent graph kernels based on frequent patterns.
Graph database indexing using structured graph decomposition
 In ICDE
, 2007
"... We introduce a novel method of indexing graph databases in order to facilitate subgraph isomorphism and similarity queries. The index is comprised of two major data structures. The primary structure is a directed acyclic graph which contains a node for each of the unique, induced subgraphs of the da ..."
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Cited by 57 (5 self)
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We introduce a novel method of indexing graph databases in order to facilitate subgraph isomorphism and similarity queries. The index is comprised of two major data structures. The primary structure is a directed acyclic graph which contains a node for each of the unique, induced subgraphs of the database graphs. The secondary structure is a hash table which crossindexes each subgraph for fast isomorphic lookup. In order to create a hash key independent of isomorphism, we utilize a codebased canonical representation of adjacency matrices, which we have further refined to improve computation speed. We validate the concept by demonstrating its effectiveness in answering queries for two practical datasets. Our experiments show that for subgraph isomorphism queries, our method outperforms existing methods by more than an order of magnitude. 1.
Mining closed relational graphs with connectivity constraints
 Proc. KDD'05
"... Relational graphs are widely used in modeling large scale networks such as biological networks and social networks. In this kind of graph, connectivity becomes critical in identifying highly associated groups and clusters. In this paper, we investigate the issues of mining closed frequent graphs wi ..."
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Cited by 49 (9 self)
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Relational graphs are widely used in modeling large scale networks such as biological networks and social networks. In this kind of graph, connectivity becomes critical in identifying highly associated groups and clusters. In this paper, we investigate the issues of mining closed frequent graphs with connectivity constraints in massive relational graphs where each graph has around 10K nodes and 1M edges. We adopt the concept of edge connectivity and apply the results from graph theory, to speed up the mining process. Two approaches are developed to handle different mining requests: CloseCut, a patterngrowth approach, and Splat, a patternreduction approach. We have applied these methods in biological datasets and found the discovered patterns interesting.
Frequent Subgraph Mining in Outerplanar Graphs
 PROC. 12TH ACM SIGKDD INT. CONF. ON KNOWLEDGE DISCOVERY AND DATA MINING
, 2006
"... In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases ..."
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Cited by 39 (7 self)
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In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we consider the class of outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for outerplanar graphs, and show that it works in incremental polynomial time for the practically relevant subclass of wellbehaved outerplanar graphs, i.e., which have only polynomially many simple cycles. We evaluate the algorithm empirically on chemo and bioinformatics applications.