J. Pei, J. Han, and L. V. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. of the 17th Int. Conf. on Data Engineering, pages 433442. IEEE Computer Society, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....than SWF. 1 Introduction Association rule mining from transaction database is an important task in data mining. The problem, first proposed by [2] is to discover associations between items from a (static) set of transactions. Many interesting works have been published to address this problem [9, 8, 11, 1, 6, 7, 10]. However, in real life applications, the transaction databases are changed with time. For example, Web log records, stock market data, and grocery sales data, etc. In these dynamic databases, the knowledge previously acquired can facilitate successive discovery processes, or become obsolete due ....

J. Pei, J. Han, and L.V.S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. of 2001 Int. Conf. on Data Engineering, 2001.

....compared to previous work. # Research conducted at Cornell University with the Intelligent Information Systems Institute 2003 Kluwer Academic Publishers. Printed in the Netherlands. 1. Introduction Mining frequent itemsets in the presence of constraints is an important problem in data mining [5, 16, 17, 18, 20]. We assume that the reader is familiar with the terminology from the association rules literature [2] The problem can be stated abstractly as follows. Let M be a finite set of items from some domain (for example, products in a grocery store) All the items have a common set of descriptive ....

....the values of the items in M . The goal of constraint based market basket analysis is then: given a set of predicates P 1 , P 2 , P n , find all subsets of M that satisfy P n . Important classes of constraints, most notably monotone and antimonotone, have been introduced by Ng et al. [17, 16, 5, 18, 20]. There exist algorithms that take advantage of each class of constraints. However, their main deficiency is that they each handle only one class of constraints e#ciently. More recently, Raedt and Kramer [22] have generalized these algorithms to allow several types of constraints, but this ....

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In ICDE 2001, pages 433--442. IEEE Computer Society, 2001.

....t #Dwith t, or more complex constraints such as the average price of the items has to be larger than c , or the variance of the prices of the items has to be smaller than c . Three important classes of constraints have been studied: monotone, antimonotone, and convertible constraints [13, 16], and each class has its own set of efficient mining algorithms [12, 16, 14, 4, 5, 6] Some of these algorithms have a certain degree of flexibility they can efficiently mine constraints from several of these classes simultaneously. For example, several algorithms can simultaneously mine ....

....price of the items has to be larger than c , or the variance of the prices of the items has to be smaller than c . Three important classes of constraints have been studied: monotone, antimonotone, and convertible constraints [13, 16] and each class has its own set of efficient mining algorithms [12, 16, 14, 4, 5, 6]. Some of these algorithms have a certain degree of flexibility they can efficiently mine constraints from several of these classes simultaneously. For example, several algorithms can simultaneously mine monotone and antimonotone constraints [14, 4, 5, 6] or mine convertible # This work was ....

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In ICDE 2001.

....value # such that #(p) # for almost all interesting patterns p and for only very few uninteresting ones. One way to augment the interestingness measure is to define additional constraints for the patterns. There has been several studies especially about structural constraints on patterns [5, 26, 40, 41, 45]. In the case of association rules structural constraints could be e.g. constraints between items. Unfortunately, defining the structural constraints may demand considerable amount of domain expertise. We suggest a complementary approach to structural constraints which can further restrict and ....

J. Pei, J. Han, and L. V. Lashmanan, Mining frequent itemsets with convertible constraints, in Proceedings of the 17th International Conference on Data Engineering, IEEE Computer Society, 2001, pp. 433--442.

....to address this problem, and to the best of our knowledge there is still no effective and efficient solution. In recent years, many constraints (apart from the traditional support and confidence constraints) are introduced into frequent itemset mining in order to find only those relevant itemsets [13, 10, 12]. On one hand, these additional constraints give the user more freedom to express his her preferences. On the other hand, however, it often prolongs the mining process because the user may want to see the results of various combinations of constraint changes by running the mining algorithm more ....

....on both synthetic data and real life data show that RM FP and RM TP dramatically outperform FP tree and Tree Projection algorithm respectively. Finally, we also address how the proposed technique can be applied to handle the changes of other types of constraints given in previous studies [13, 10, 12]. 2. Related work Frequent itemset mining has been studied extensively in the past e.g. in [3, 16, 1, 9, 15, 4, 5] Most current algorithms are variations of the Apriori algorithm [3] They use support based generate and test approach to find all the frequent itemsets. Recently, some tree based ....

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J. Pei, J. Han, and L.V.S.Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. ICDE, 2001.

....generalized. Problem 1 Consider 0 1 data and a class P of patterns de ned as boolean expressions. Under what conditions for P is there an ecient algorithm for nding those patterns 2 P that are true for at least a given fraction of rows of the data set Many results exist already; see, e.g. [9, 40, 39]. In pattern discovery one often has to analyze di erent but similar data sets: transactions from last month and from this month etc. Problem 2 Given a class P of patterns and two data sets d and d , nd a good way of representing the patterns of P that are true in d , assuming the user ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In ICDE 2001, pages 433-442, 2001.

....prune its search space. We complement a theoretical analysis and proof of correctness of DualMiner with an experimental study that shows the e#cacy of DualMiner compared to previous work. 1. INTRODUCTION Mining frequent itemsets in the presence of constraints is an important data mining problem [5, 9, 10, 11, 12]. We assume that the reader is familiar with the terminology from the association rules literature [2] The problem can be stated abstractly as follows. Let M be a finite set of items from some domain (for example, products in a grocery store) All the items have a common set of descriptive ....

....Alberta, Canada Copyright 2002 ACM 1 58113 567 X 02 0007 . 5.00. Given a set of predicates P1 , P2 , Pn , find all sets in the powerset of M that satisfy P1 P2 Pn . Important classes of constraints, most notably monotone and antimonotone, have been introduced by Ng et al. [10, 9, 5, 11, 12] and there exist algorithms that are designed to take advantage of each class of constraints. However, the main deficiency in such algorithms is that they e#ciently handle only one class of constraints. More recently, Raedt and Kramer [13] have generalized these algorithms to allow several types ....

[Article contains additional citation context not shown here]

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In ICDE 2001.

.... can be considered as a generalization of several algorithms like [26, 10, 20] Conjunctions of monotone and anti monotone constraints encompass every kind of constraints that have been pushed inside a levelwise algorithm (another kind of interesting constraint, the convertible constraints [23], can be pushed in depth rst exploration algorithms) The framework of succinct constraints introduced in [20] allows to nd an e ective generation procedure (i.e. an e ective computation of the negative border Bd C 0 in procedure generate m (L; k) 3.4 Eciency Issues Pushing ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proceedings of the 17th International Conference on Data Engineering ICDE'01, Heidelberg, Germany, Apr. 2001. IEEE Computer Society Press.

....by several algorithms [18, 8, 13] and can be considered as a generalization of them. Conjunctions of monotone and antimonotone constraints encompass every kind of constraints that have been pushed inside a levelwise algorithm (another kind of interesting constraint, the convertible constraints [16], can be pushed in depth first exploration algorithms) The framework of succinct constraints introduced in [13] allows to find an effective generation procedure (i.e. an effective computation of the negative border Bd C of Theorem 1) 4. Revisiting the CLOSE Algorithm It is now interesting ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. ICDE'01, Heidelberg, Germany, 2001.

.... can be considered as a generalization of several algorithms like [26, 10, 20] Conjunctions of monotone and anti monotone constraints encompass every kind of constraints that have been pushed inside a levelwise algorithm (another kind of interesting constraint, the convertible constraints [23], can be pushed in depth rst exploration algorithms) The framework of succinct constraints introduced in [20] allows to nd an e ective generation procedure (i.e. an e ective computation of the negative border # am in procedure generate m (L, k) 3.4 E ciency Issues Pushing anti monotone ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proceedings of the 17th International Conference on Data Engineering ICDE'01, Heidelberg, Germany, Apr. 2001. IEEE Computer Society Press.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. 2001 Int. Conf. Data Engineering (ICDE'01), pages 433--332, Heidelberg, Germany, April 2001.

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J. Pei, J. Han, and L.V.S. Lakshmanan, "Mining Frequent Itemsets with Convertible Constraints," Proc. 2001.

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J. Pei, J. Han, and L.V.S. Lakshmanan, "Mining Frequent Itemsets with Convertible Constraints," Proc. Int'l Conf. Data Eng., pp. 433332, Apr. 2001.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. 2001 Int. Conf. Data Engineering (ICDE'01), pages 433--332, Heidelberg, Germany, April 2001.

....technique relies on a large minimum support k. Unlike [6] the work proposed here is applicable, with or without a minimum support, to a general class of constraints, rather than specific to a particular constraint. This work is related to constrained association mining in transactional databases [8, 9]. 8] considers constraints of anti monotonicity, monotonicity, and succinctness. We consider constraints without such properties. 8] uses item based aggregates where the measure is associated with items (i.e. dimension values in our setting) In contrast, we adopt tuple based aggregates, ....

....aggregates where the measure is associated with items (i.e. dimension values in our setting) In contrast, we adopt tuple based aggregates, similar to SQL aggregates. This difference essentially affects the applicability of pushing techniques. For example, by adopting item based aggregates, [9] is able to push avg(v) through the item order induced by the associated measure, but that technique is not applicable to tuple based aggregates because no such order exists. Some other constraints are pushed in [2, 10, 11] using constraint specific techniques, but they are quite different ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In ICDE, 2001.

....like [15] have shown that, by doing so, the total number of patterns and rules can be reduced substantially, especially in dense data sets. Second, constraints can be used to capture users focus, and effective strategies have been developed to push various constraints deep into the mining process [11, 9, 13]. Even though these approaches are useful, they may not be powerful enough in many cases. The compression by the closed pattern approach may not be so effective since there often exist slightly different counts between superand sub patterns. Constraint based mining, though useful, can hardly be ....

J. Pei, J. Han, L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In ICDE'01.

....databases. For other constraints, whether the constraint is satisfied can be determined by the frequent patterns themselves, without referring to the support counting process. 3. ACLASSICALFRAMEWORKOFCHARACTERIZATION OF CONSTRAINTS In recent studies of constrained frequent pattern mining [6, 7, 8], constraints are characterized based on the notion of monotonicity, anti monotonicity, succinctness, and whether they can be transformed into these categories if they do not belong to them. This has become a classical framework for constraint based frequent pattern mining. Can we extend this ....

....database SDB. Constraint C cannot be pushed naively into the PrefixSpan mining process. For example # = cannot be discarded even avg(#) 25, since by appending more elements to #, we may have # # = 10 20 10# and avg(# # ) 25. Also, one can easily verify C is not prefixmonotone. In [8], a technique is developed to push convertible constraints, like avg(X) 25, into frequent pattern mining on transactional databases. The general idea is to use a proper order of frequent items, like value descending order for constraint avg(X) v, such that the list of frequent items ....

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J. Pei et al. Mining frequent itemsets with convertible constraints. ICDE'01.

....and perform probe constrained mining to find the support only related to those itemsets. 4) As an alternative to the above, one can set min #= 2, which will derive the patterns readily for all the combinations of association rules. 5. 3 Pushing constraints into TFP mining Constraint based mining [4, 6] is essential to top k mining since users may always want to put constraints on the data and rules to be mined. We examine how di#erent kinds of constraints can be pushed into the top k frequent closed pattern mining. First, succinct and anti monotone constraints can be pushed deep into the ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. ICDE'01.

....method. Its structure and space preserving mining methodology may have strong impact on the development of new, efficient and scalable data mining methods for mining other kinds of patterns, such as closed itemsets [11] max patterns [4] sequential patterns [14, 12] constraintbased mining [9, 10], etc. This should be an interesting direction for further study. ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. In ICDE'01, pages 433--332.

....preprocessing step for subsequent statistical studies on mined interesting gradients or rules. Our study is also closely related to (1) data cube and iceberg cube computation methods proposed in previous studies, such as [1, 4, 6, 3, 8] as well as (2) constraintbased data mining methods, such as [13, 10, 5, 7, 11]. This study can be considered as an extension and integration of both mechanisms towards efficient, multi dimensional, constrained gradient analysis. 7 Conclusions In this paper, we have studied issues and methods on efficient mining of multi dimensional, constrained gradients in data cubes. ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. ICDE'01.

....data mining algorithms retrieve the complete answer set based on a user specified support threshold. However, often the overwhelming size of the answer set returned is not easy for users to digest. This motivates constrained based mining ( RVA97] NLHP98] BAG99] LNHP99] GLW00] PH00] [PHL01]) which allows users to give more specification on an interesting answer set such that only answers that are interesting to the users will be returned. Also, these user specified constraints can be exploited in algorithms for efficient pruning. The notion of anti monotonicity was introduced by ....

....mining. PH00] introduces a new class of constraints, called convertible constraints, which includes AVG(c) v constraint for association mining. The proposed technique [PH00] requires average measures arranged in value sorted order. This limitation makes it difficult to realize in data cubes. [PHL01] carried the study further to explore the possibility to incorporate the tough constraints, including AVG(S) q v, SUM(S) q v (S can contain items of arbitrary values) where q , within frequent pattern algorithms. These so called tough constraints do not exhibit monotonicity property that ....

Jian Pei, Jiawei Han, Laks V.S. Lakshmanan. Mining Frequent Itemsets with Convertible Constraints. In Proceedings of the 17 th International Conference on Data Engineering (ICDE'01), April 2-6, 2001, Heidelberg, Germany.

....preprocessing step for subsequent statistical studies on mined interesting gradients or rules. Our study is also closely related to (1) data cube and iceberg cube computation methods proposed in previous studies, such as [1, 4, 6, 3, 8] as well as (2) constraintbased data mining methods, such as [13, 10, 5, 7, 11]. This study can be considered as an extension and integration of both mechanisms towards efficient, multi dimensional, constrained gradient analysis. 7 Conclusions In this paper, we have studied issues and methods on efficient mining of multi dimensional, constrained gradients in data cubes. ....

J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent itemsets with convertible constraints. ICDE'01.

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J. Pei, J. Han, and L. V. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. of the 17th Int. Conf. on Data Engineering, pages 433442. IEEE Computer Society, 2001.

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Jian Pei, Jiawei Han, and Laks V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In Proceedings of the 17th International Conference on Data Engineering, pages 433--442, 2001.

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J. Pei, J. Han, and L.V.S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proceedings of the 17th International Conference on Data Engineering, pages 433-442. IEEE Computer Society, 2001.

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J. Pei, J. Han, and L. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proc. 2001.

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Pei J., Han J., Lakshmanan L.: Mining Frequent Itemsets with Convertible Constraints. Proceedings of the 17th ICDE Conference (2001)

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J. Pei, J. Han, and L.V.S. Lakshmanan. Mining frequent itemsets with convertible constraints. In Proceedings of the 17th International Conference on Data Engineering, pages 433--442. IEEE Computer Society, 2001.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In (ICDE'01), pages 433--442, 2001.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In (ICDE'01), pages 433--442, 2001.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In Proc. of ICDE'01.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In ICDE'01, pages 433--442, 2001.

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Jian Pei, Jiawei Han, Laks V. S. Lakshmanan, Mining Frequent Item Sets with Convertible Constraints, ICDE'01, April, 2001.

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J. Pei, J. Han, L. Lakshmanan, Mining Frequent Itemsets with Convertible Constraints. Proceedings of the 17th ICDE Conference, 2001.

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Jian Pei, Jiawei Han, Laks V. S. Lakshmanan, Mining Frequent Item Sets with Convertible Constraints, ICDE'01, April, 2001.

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J. Pei, J. Han, and L. V. S. Lakshmanan. Mining frequent item sets with convertible constraints. In (ICDE'01), pages 433--442, 2001.

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J. Pei, J. Han, and L.V.S. Lakshmanan. Mining Frequent Itemsets with Convertible Constraints. Proc. of 2001 Int. Conf. on Data Engineering,200#.

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