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77
Frequent Subgraph Discovery
, 2001
"... Over the years, frequent itemset discovery algorithms have been used to solve various interesting problems. As data mining techniques are being increasingly applied to nontraditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of th ..."
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Cited by 406 (10 self)
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Over the years, frequent itemset discovery algorithms have been used to solve various interesting problems. As data mining techniques are being increasingly applied to nontraditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the database objects. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a computationally efficient algorithm for finding all frequent subgraphs in large graph databases. We evaluated the performance of the algorithm by experiments with synthetic datasets as well as a chemical compound dataset. The empirical results show that our algorithm scales linearly with the number of input transactions and it is able to discover frequent subgraphs from a set of graph transactions reasonably fast, even though we have to deal with computationally hard problems such as canonical labeling of graphs and subgraph isomorphism which are not necessary for traditional frequent itemset discovery.
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.
Graph mining: laws, generators, and algorithms
 ACM COMPUT SURV (CSUR
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in ..."
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Cited by 132 (7 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in realworld graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
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.
Substructure similarity search in graph databases
 In SIGMOD
, 2005
"... Advanced database systems face a great challenge raised by the emergence of massive, complex structural data in bioinformatics, cheminformatics, and many other applications. The most fundamental support needed in these applications is the efficient search of complex structured data. Since exact mat ..."
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Cited by 90 (6 self)
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Advanced database systems face a great challenge raised by the emergence of massive, complex structural data in bioinformatics, cheminformatics, and many other applications. The most fundamental support needed in these applications is the efficient search of complex structured data. Since exact matching is often too restrictive, similarity search of complex structures becomes a vital operation that must be supported efficiently. In this paper, we investigate the issues of substructure similarity search using indexed features in graph databases. By transforming the edge relaxation ratio of a query graph into the maximum allowed missing features, our structural filtering algorithm, called Grafil, can filter many graphs without performing pairwise similarity computations. It is further shown that using either too few or too many features can result in poor filtering performance. Thus the challenge is to design an effective feature set selection strategy for filtering. By examining the effect of different feature selection mechanisms, we develop a multifilter composition strategy, where each filter uses a distinct and complementary subset of the features. We identify the criteria to form effective feature sets for filtering, and demonstrate that combining features with similar size and selectivity can improve the filtering and search performance significantly. Moreover, the concept presented in Grafil can be applied to searching approximate nonconsecutive sequences, trees, and other complicated structures as well. 1.
Fgindex: towards verificationfree query processing on graph databases
 in SIGMOD, 2007
"... Graphs are prevalently used to model the relationships between objects in various domains. With the increasing usage of graph databases, it has become more and more demanding to efficiently process graph queries. Querying graph databases is costly since it involves subgraph isomorphism testing, whic ..."
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Cited by 77 (10 self)
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Graphs are prevalently used to model the relationships between objects in various domains. With the increasing usage of graph databases, it has become more and more demanding to efficiently process graph queries. Querying graph databases is costly since it involves subgraph isomorphism testing, which is an NPcomplete problem. In recent years, some effective graph indexes have been proposed to first obtain a candidate answer set by filtering part of the false results and then perform verification on each candidate by checking subgraph isomorphism. Query performance is improved since the number of subgraph isomorphism tests is reduced. However, candidate verification is still inevitable, which can be expensive when the size of the candidate answer set is large. In this paper, we propose a novel indexing technique that constructs a nested invertedindex, called FGindex, based on the set of Frequent subGraphs (FGs). Given a graph query that is an FG in the database, FGindex returns the exact set of query answers without performing candidate verification. When the query is an infrequent graph, FGindex produces a candidate answer set which is close to the exact answer set. Since an infrequent graph means the graph occurs in only a small number of graphs in the database, the number of subgraph isomorphism tests is small. To ensure that the index fits into the main memory, we propose a new notion of δTolerance Closed Frequent Graphs (δTCFGs), which allows us to flexibly tune the size of the index in a parameterized way. Our extensive experiments verify that query processing using FGindex is orders of magnitude more efficient than using the stateoftheart graph index.
Summarizing itemset patterns: a profilebased approach
 In KDD
, 2005
"... Frequentpattern mining has been studied extensively on scalable methods for mining various kinds of patterns including itemsets, sequences, and graphs. However, the bottleneck of frequentpattern mining is not at the efficiency but at the interpretability, due to the huge number of patterns generat ..."
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Cited by 67 (9 self)
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Frequentpattern mining has been studied extensively on scalable methods for mining various kinds of patterns including itemsets, sequences, and graphs. However, the bottleneck of frequentpattern mining is not at the efficiency but at the interpretability, due to the huge number of patterns generated by the mining process. In this paper, we examine how to summarize a collection of itemset patterns using only K representatives, a small number of patterns that a user can handle easily. The K representatives should not only cover most of the frequent patterns but also approximate their supports. A generative model is built to extract and profile these representatives, under which the supports of the patterns can be easily recovered without consulting the original dataset. Based on the restoration error, we propose a quality measure function to determine the optimal value of parameter K. Polynomial time algorithms are developed together with several optimization heuristics for efficiency improvement. Empirical studies indicate that we can obtain compact summarization in real datasets.
Graph indexing: Tree + delta >= graph
 In VLDB
, 2007
"... Recent scientific and technological advances have witnessed an abundance of structural patterns modeled as graphs. As a result, it is of special interest to process graph containment queries effectively on large graph databases. Given a graph database G, and a query graph q, the graph containment qu ..."
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Cited by 53 (6 self)
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Recent scientific and technological advances have witnessed an abundance of structural patterns modeled as graphs. As a result, it is of special interest to process graph containment queries effectively on large graph databases. Given a graph database G, and a query graph q, the graph containment query is to retrieve all graphs in G which contain q as subgraph(s). Due to the vast number of graphs in G and the nature of complexity for subgraph isomorphism testing, it is desirable to make use of highquality graph indexing mechanisms to reduce the overall query processing cost. In this paper, we propose a new costeffective graph indexing method based on frequent treefeatures of the graph database. We analyze the effectiveness and efficiency of tree as indexing feature from three critical aspects: feature size, feature selection cost, and pruning power. In order to achieve better pruning ability than existing graphbased indexing methods, we select, in addition to frequent treefeatures (Tree), a small number of discriminative graphs (∆) on demand, without a costly graph mining process beforehand. Our study verifies that (Tree+∆) is a better choice than graph for indexing purpose, denoted (Tree+ ∆ ≥Graph), to address the graph containment query problem. It has two implications: (1) the index construction by (Tree+∆) is efficient, and (2) the graph containment query processing by (Tree+∆) is efficient. Our experimental studies demonstrate that (Tree+∆) has a compact index structure, achieves an order of magnitude better performance in index construction, and most importantly, outperforms uptodate graphbased indexing methods: gIndex and CTree, in graph containment query processing. 1.