Laks V. S. Lakshmanan, Raymond Ng, Jiawei Han, and Alex Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings of the 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Other types of constraints were introduced later by Ng et al. 17, 16] These papers introduced the concepts of antimonotone and succinct constraints and presented methods for using them to prune the search space. These classes of constraints were also studied in the case of 2 variable constraints [14] and along with monotone constraints were further generalized and studied by Pei et al. 20, 18] Boulicant and Jeudy present algorithms for mining frequent itemsets with both antimonotone and non antimonotone constraints [6, 7] However they assume that the minimal itemsets satisfying the ....

L. V. S. Lakshmanan, R. T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Delis et al. [9], pages 157--168.

....or in sequence. Since the earlier work in [1] sev eral technologies on association rule mining have been devel oped, including: 1) association rule mining [5, 14] 2) incremental updating [8] 3) mining of generalized [16] multidimensional rules [17] 4) constraint based rule mining [6, 10] and multiple minimum supports issues [11] 5) temporal association rule mining [7, 9] 6) frequent episodes discovery [13] and (7) sequential patterns mining [2, 15] While the discovery of association rules and sequential patterns among the transaction data in a huge commerce database has ....

L. V. S. Lakshmanan, R. Ng, J. Hah, and A. Pang. Optimization of Constrained Frequent Set Queries with 2-Variable Constraints. Proc. of ACM-$IGMOD99, pages 157-168, June 1999.

....Other types of constraints were introduced later by Ng et al. 13, 12] These papers introduced the concepts of antimonotone and succinct constraints and presented methods for using them to prune the search space. These classes of constraints were also studied in the case of 2 variable constraints [10] and along with monotone constraints were further generalized and studied by Pei et al. 16, 14] Boulicant and Jeudy present algorithms for mining frequent itemsets with both antimonotone and non antimonotone constraints [4, 5] However they assume that the minimal itemsets satisfying the ....

L. V. S. Lakshmanan, R. T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Delis et al. [7], pages 157--168.

....patterns or rules will be derived. During the last four years, two promising issues have been investigated to tackle these problems. One can assume that only a subset of the collection of frequent itemsets is interesting: it leads to constraint based extraction of the frequent itemsets [26, 20, 16]. These studies have considered various kinds of constraints, including syntactic constraints (e.g. an item must not appear in the itemsets) and constraints related to the so called objective measures of itemset interestingness (e.g. the itemsets must be frequent) Using constraints enables to ....

....to push the constraints before Step 3. Since the more expensive step of this process is the generation of frequent itemsets (Step 1) the constraints should be pushed during Step 1. 3 Pushing Constraints Strategies for pushing constraints have been studied for association rule mining (e.g. [26, 20, 16]) correlation discovery [11] sequential pattern mining (e.g. 28] etc. However, not all constraints can be pushed. Assume that one wants to perform the association rule mining task with a constraint C = C 1 C 2 where C 1 can be pushed during the itemset extraction and C 2 can not. A strategy ....

L. V. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings 25 pages 157-168, Philadelphia, USA, 1999. ACM Press.

....on the mining data. If we remember the KDD process exemplarily described in Section 3 it becomes clear that even interruptions of the analysts work of a single minute are already problematic. Some authors tackle this problem by pushing constraints on the result set into the mining algorithm [22, 24, 25, 29]. Actually the performance improves but the run times are still far from allowing true interactivity. Furthermore the constraint result set will probably answer fewer of the analysts questions and therefore will provoke additional further mining runs. The solution that we propose is to do exactly ....

L. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries: 2-var constraints. In 3rd SIGMOD'98 Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD), pages 157-168, Seattle, WA, June 1998.

....patterns or rules will be derived. During the last three years, two promising issues have been investigated to tackle these problems. First, one can assume that only a subset of the collection of frequent itemsets is interesting: it leads to constraintbased extraction of the frequent itemsets [18, 13, 10, 7]. These studies have considered various kinds of constraints, including syntactic constraints (e.g. an item must not appear in the itemsets) and constraints related to the socalled objective measures of itemset interestingness (e.g. the itemsets must be frequent) Using constraints enables to ....

....i.e. not to apply a simple generate and test strategy. Nice results have been discovered concerning the so called anti monotone, succinct and monotone constraints [13, 7] i.e. a wide range of constraints. This framework has been also studied for other kinds of properties like rules [10] or correlations [9] Another promising approach concerns the condensed representation of frequent itemsets [11] The intuition is that instead of mining all the frequent patterns, one can extract a particular subset of the frequent pattern collection such that it is possible to regenerate from ....

L. V. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings of ACM SIGMOD Conference on Management of Data (SIGMOD'99), pages 157 -- 168, Philadelphia, USA, 1999. ACM Press.

....patterns or rules will be derived. During the last four years, two promising issues have been investigated to tackle these problems. One can assume that only a subset of the collection of frequent itemsets is interesting: it leads to constraint based extraction of the frequent itemsets [26, 20, 16]. These studies have considered various kinds of constraints, including syntactic constraints (e.g. an item must not appear in the itemsets) and constraints related to the so called objective measures of itemset interestingness (e.g. the itemsets must be frequent) Using constraints enables to ....

....to push the constraints before Step 3. Since the more expensive step of this process is the generation of frequent itemsets (Step 1) the constraints should be pushed during Step 1. 3 Pushing Constraints Strategies for pushing constraints have been studied for association rule mining (e.g. [26, 20, 16]) correlation discovery [11] sequential pattern mining (e.g. 28] etc. However, not all constraints can be pushed. Assume that one wants to perform the association rule mining task with a constraint 2 where 1 can be pushed during the itemset extraction and 2 can not. A strategy ....

L. V. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings pages 157168, Philadelphia, USA, 1999. ACM Press.

....and generalization do not apply for two variable constraints. Specialization does not apply since a non qualifying 1 tuple does not allow us to draw any conclusions about either of the attributes occurring in the output. Dealing with two variable constraints is hard in other related problems too [LNHP99] It would be useful to come up with applicable optimizations rather than having to resort to the naive strategy of checking if the predicate holds for each computed datacube tuple. 116 Appendix A A.1 Table of Symbols Number of dimensions d Number of slots in the level 2 store T Number of ....

L. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings of the

....resampling. Extensions of these statistical simulation and sampling techniques are needed to validate cubegrades also. Most of the measures of interest in all these works were based on count measure. The only works that we are aware of that incorporate measures other than count are [NLHP98a, LNHP99] The objective in both of the papers is to extend the framework of rule querying in market basket data with new aggregate constraints like SUM, MIN, MAX and AVG on the basket items. In [NLHP98a] constraints of the form A(X) # c are considered and in the second paper more complicated ....

L.V.S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings of ACM SIGMOD Conference on Management of Data (SIGMOD'99), pages 157 -- 168, Zurich, Switzerland, Sept 1999.

....query optimizers must be able to decide which data mining optimization techniques are effective for a given data mining query. In the domain of mining frequent itemsets and association rules, there has been a number of recent papers relating to the second question raised above. Lakshmanan et al. [6, 11] have introduced the paradigm of constrained frequent set queries. They point out that users typically want to impose constraints on the itemsets to be discovered (for example, itemsets must contain milk ) they then explore the relationships between the properties of constraints on the one hand ....

L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proc. ACM SIGMOD Int. Conf. Management of Data, pages 157--168, 1999.

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L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proc. 1999 ACM-SIGMOD Int. Conf. Management of Data (SIGMOD'99), pages 157--168, Philadelphia, PA, June 1999.

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L.V.S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings of the 1999.

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L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proc. 1999.

....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 ....

L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In SIGMOD'99.

....and presents a query optimizer that generates ccc optimal strategies for a large class of constraints. Section 7 presents experimental results demonstrating the effectiveness of the optimizations. Section 8 discusses open research problems. For lack of space, the reader is referred to [13] for complete details of the proofs. 2 Background Readers familiar with [15] can skip this section. A CFQ is a query of the form (S, T) I , where is a conjunction of domain, class, and aggregation constraints. For our exampies below, we assume the transaction database trans (TID, Itemset) with ....

....C1( sound tight C2 Figure 3: Quasi succinctness: Reduction of min 0 and max( Constraints is one of = and S.A and T.B are in the same domain. Again because there are many combinations, we only summarize a few cases in Figures I and 3. Other cases not shown can be handled similarly [13]. In terms of for mal results, as shown in the theorem below, in each case, the accompanying 1 var constraints are guaranteed to be succinct, sound and tight pruning conditions. For lack of space, we only show a proof sketch for one 2 var constraint, C max(S.A) max(T.B) It will become ....

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L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Op- timization of constrained frequent set queries: 2-var constraints. Technical Report, Department of Computer Science, University of British Columbia, 1998.

....whose frequencies are needed, are conjunctions of atomic patterns. A prime example is given by the frequent set concept underlying association rules [2, 3] Moreover, the patterns defined for correlation [6, 7] causality [18] sequential patterns [4] episodes [13] constrained frequent sets [11, 14, 19], long patterns [1, 5] closed sets [16] and many other important data mining tasks have the same basic form. In all these cases, we have instances of the following abstract problem. Given a collection P of atomic patterns or conditions, compute for collections S P the support sup(S) of S. The ....

L.V.S. Lakshmanan, R. Ng, et al. Optimization of constrained frequent set queries with 2-variable constraints. In Proc. SIGMOD 1999, pp 157--168.

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Laks V. S. Lakshmanan, Raymond Ng, Jiawei Han, and Alex Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Proceedings of the 1999.

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L.V.S. Lakshmanan, R.T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In A. Delis, C. Faloutsos, and S. Ghandeharizadeh, editors, Proceedings of the 1999.

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L.V.S. Lakshmanan, R.T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In Delis et al.

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L. V. S. Lakshmanan, R. T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. SIGMOD Record (ACM Special Interest Group on Management of Data), 28(2), 1999.

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L. V. S. Lakshmanan, R. T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. SIGMOD Record (ACM Special Interest Group on Management of Data), 28(2), 1999.

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L.V.S. Lakshmanan, R.T. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. In A. Delis, C. Faloutsos, and S. Ghandeharizadeh, editors, Proceedings of the 1999.

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L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of Constrained Frequent Set Queries with 2-Variable Constraints. Proc. of 1999 ACM-SIGMOD Conf. on Management of Data, pages #57---#68, June #999.

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L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang, "Optimization of Constrained Frequent Set Queries with 2-variable Constraints," Proceedings of the ACM SIGMOD, Philadelphia, PA, June 1999, pp. 157-168.

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L. V. S. Lakshmanan, R. Ng, J. Han, and A. Pang. Optimization of constrained frequent set queries with 2-variable constraints. SIGMOD'99.

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