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17
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 390 (14 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.
A tree projection algorithm for generation of frequent itemsets
 Journal of Parallel and Distributed Computing
, 2000
"... In this paper we propose algorithms for generation of frequent itemsets by successive construction of the nodes of a lexicographic tree of itemsets. We discuss di erent strategies in generation and traversal of the lexicographic tree such as breadth rst search, depth rst search or a combination of ..."
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Cited by 187 (2 self)
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In this paper we propose algorithms for generation of frequent itemsets by successive construction of the nodes of a lexicographic tree of itemsets. We discuss di erent strategies in generation and traversal of the lexicographic tree such as breadth rst search, depth rst search or a combination of the two. These techniques provide di erent tradeo s in terms of the I/O, memory and computational time requirements. We use the hierarchical structure of the lexicographic tree to successively project transactions at each node of the lexicographic tree, and use matrix counting on this reduced set of transactions for nding frequent itemsets. We tested our algorithm on both real and synthetic data. We provide an implementation of the tree projection method which is up to one order of magnitude faster than other recent techniques in the literature. The algorithm has a well structured data access pattern which provides data locality and reuse of data for multiple levels of the cache. We also discuss methods for parallelization of the
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 112 (9 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.
LPMiner: An Algorithm for Finding Frequent Itemsets Using LengthDecreasing Support Constraint
, 2001
"... Over the years, a variety of algorithms for finding frequent itemsets in very large transaction databases have been developed. The key feature in most of these algorithms is that they use a constant support constraint to control the inherently exponential complexity of the problem. In general, items ..."
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Cited by 40 (19 self)
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Over the years, a variety of algorithms for finding frequent itemsets in very large transaction databases have been developed. The key feature in most of these algorithms is that they use a constant support constraint to control the inherently exponential complexity of the problem. In general, itemsets that contain only a few items will tend to be interesting if they have a high support, whereas long itemsets can still be interesting even if their support is relatively small. Ideally,wedesiretohave an algorithm that finds all the frequent itemsets whose support decreases as a function of their length. In this paper we present an algorithm called LPMiner, that finds all itemsets that satisfy a lengthdecreasing support constraint. Our experimental evaluation shows that LPMiner is up to two orders of magnitude faster than the FPgrowth algorithm for finding itemsets at a constant support constraint, and that its runtime increases gradually as the average length of the transactions (and the discovered itemsets) increases. 1
SLPMiner: An Algorithm for Finding Frequent Sequential Patterns Using LengthDecreasing Support Constraint
 In Proceedings of the 2nd IEEE International Conference on Data Mining (ICDM
, 2002
"... Over the years, a variety of algorithms for finding frequent sequential patterns in very large sequential databases have been developed. The key feature in most of these algorithms is that they use a constant support constraint to control the inherently exponential complexity of the problem. In gene ..."
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Cited by 39 (5 self)
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Over the years, a variety of algorithms for finding frequent sequential patterns in very large sequential databases have been developed. The key feature in most of these algorithms is that they use a constant support constraint to control the inherently exponential complexity of the problem. In general, patterns that contain only a few items will tend to be interesting if they have a high support, whereas long patterns can still be interesting even if their support is relatively small. Ideally, we desire to have an algorithm that finds all the frequent patterns whose support decreases as a function of their length. In this paper we present an algorithm called SLPMiner, that finds all sequential patterns that satisfy a lengthdecreasing support constraint. SLPMiner combines an efficient databaseprojectionbased approach for sequential pattern discovery with three effective database pruning methods that dramatically reduce the search space. Our experimental evaluation shows that SLPMiner, by effectively exploiting the lengthdecreasing support constraint, is up to two orders of magnitude faster, and its runtime increases gradually as the average length of the sequences (and the discovered frequent patterns) increases.
Discovering Frequent Geometric Subgraphs
 In IEEE Intl. Conference on Data Mining ’02
, 2002
"... 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 ..."
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Cited by 37 (1 self)
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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 e#cient algorithm for finding frequent geometric subgraphs in a large collection of geometric graphs. Our algorithm is able to discover geometric subgraphs that can be rotation, scaling and translation invariant, and it can accommodate inherent errors on the coordinates of the vertices. We evaluated the performance of the algorithm using a large database of over 20,000 real two dimensional chemical structures, and our experimental results show that our algorithms requires relatively little time, can accommodate low support values, and scales linearly on the number of transactions.
Efficient Closed Pattern Mining in the Presence of Tough Block Constraints
 In proceedings of ACM SIGKDD
, 2004
"... In recent years, various constrained frequent pattern mining problem formulations and associated algorithms have been developed that enable the user to specify various itemsetbased constraints that better capture the underlying application requirements and characteristics. In this paper we introduce ..."
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Cited by 15 (2 self)
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In recent years, various constrained frequent pattern mining problem formulations and associated algorithms have been developed that enable the user to specify various itemsetbased constraints that better capture the underlying application requirements and characteristics. In this paper we introduce a new class of block constraints that determine the significance of an itemset pattern by considering the dense block that is formed by the pattern's items and its associated set of transactions. Block constraints provide a natural framework by which a number of important problems can be specified and make it possible to solve numerous problems on binary and realvalued datasets. However, developing computationally e#cient algorithms to find these block constraints poses a number of challenges as unlike the di#erent itemsetbased constraints studied earlier, these block constraints are tough as they are neither antimonotone, monotone, nor convertible. To overcome this problem, we introduce a new class of pruning methods that can be used to significantly reduce the overall search space and make it possible to develop computationally e#cient block constraint mining algorithms. We present an algorithm called CBMiner that takes advantage of these pruning methods to develop an algorithm for finding the closed itemsets that satisfy the block constraints. Our extensive performance study shows that CBMiner generates more concise result set and can be order(s) of magnitude faster than the traditional frequent closed itemset mining algorithms.
Finding Frequent Patterns Using LengthDecreasing Support Constraints
"... Finding prevalent patterns in large amount of data has been one of the major problems in the area of data mining. ..."
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Cited by 6 (0 self)
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Finding prevalent patterns in large amount of data has been one of the major problems in the area of data mining.
Frequent Closed Itemset Mining Using Prefix Graphs with an Efficient FlowBased Pruning Strategy
 In Proc. ICDM 2006
, 2006
"... This paper presents PGMiner, a novel graphbased algorithm for mining frequent closed itemsets. Our approach consists of constructing a prefix graph structure and decomposing the database to variable length bit vectors, which are assigned to nodes of the graph. The main advantage of this representat ..."
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Cited by 4 (1 self)
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This paper presents PGMiner, a novel graphbased algorithm for mining frequent closed itemsets. Our approach consists of constructing a prefix graph structure and decomposing the database to variable length bit vectors, which are assigned to nodes of the graph. The main advantage of this representation is that the bit vectors at each node are relatively shorter than those produced by existing vertical mining methods. This facilitates fast frequency counting of itemsets via intersection operations. We also devise several internode and intranode pruning strategies to substantially reduce the combinatorial search space. Unlike other existing approaches, we do not need to store in memory the entire set of closed itemsets that have been mined so far in order to check whether a candidate itemset is closed. This dramatically reduces the memory usage of our algorithm, especially for low support thresholds. Our experiments using synthetic and realworld data sets show that PGMiner outperforms existing mining algorithms by as much as an order of magnitude and is scalable to very large databases. 1.
Discovering geometric frequent subgraph
 In IEEE International Conference on Data Mining
, 2002
"... 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 dat ..."
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Cited by 2 (2 self)
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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 frequent geometric subgraphs in a large collection of geometric graphs. Our algorithm is able to discover geometric subgraphs that can be rotation, scaling and translation invariant, and it can accommodate inherent errors on the coordinates of the vertices. We evaluated the performance of the algorithm using a large database of over 20,000 real two dimensional chemical structures, and our experimental results show that our algorithms requires relatively little time, can accommodate low support values, and scales linearly on the number of transactions. 1