D-I. Lin and Z.M. Kedem, "Pincer-Search: A New Algorithm for Discovering the Maximum Frequent Set," Proc. Sixth Int'l Conf. Extending Database Technology, Mar. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....typically finds an exponen tial number of frequent itemsets. For example, finding long itemsets of length 30 or 40 is not uncommon [4] Methods for finding the maximal elements include AllMFS [9] which is a randomized algorithm to discover maximal frequent itemsets. The Pincer Search algorithm [12] not only constructs the candidates in a bottomup manner like Apriori, but also starts a top down search at the same time. This can help in reducing the number of database scans. MaxMiner [4] is another algorithm for finding the maximal elements. It uses e# cient pruning based on lookaheads to ....

....same for single items in both runs. However, we find that while the tidset size remains more or less constant over the di#erent lengths, the di#set size reduces drastically. For example, the average di#set size falls below 1 for the last few lengths (over the length interval [11 16] for chess, [9 12] for connect, 7 17] for mushroom, 8 15] for pumsb , 8 for pumsb, 9 11] for T10, 12 14] for T20) The only exception is T40 where the di#set length is 5 for the longest patterns. However, over the same interval range the avg. tidset size is 1682 for chess, 61325 for connect, 495 for mushroom, ....

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D-I. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In 6th Intl. Conf. Extending Database Technology, March 1998.

.... rst as a sub problem of mining association rules, but then it turned out that frequent patterns solve a variety of problems: mining sequential patterns [AS95] episodes [MTV97] association rules [AS94] correlations [BMS97, SBM98] multi dimensional patterns [KHC97, LSW97] maximal patterns [ZPOL97, LK98] and several other important knowledge discovery tasks [HPY00] Since the complexity of this problem is exponential in the size of the binary database input relation and since this relation has to be scanned several times during the process, ecient algorithms for mining frequent patterns are ....

D. Lin and Z. M. Kedem. Pincer-Search: A new algorithm for discovering the maximum frequent set. Proc. EBDT conf., pp 105-119, March 1998.

.... frequent patterns arose rst as a sub problem of mining association rules [1] but it then turned out to be present in a variety of problems [18] mining sequential patterns [3] episodes [26] association rules [2] correlations [10, 37] multi dimensional patterns [21, 22] maximal patterns [8, 53, 23], closed patterns [47, 31 33] Since the complexity of this problem is exponential in the size of the binary database input relation and since this relation has to be scanned several times during the process, ecient algorithms for mining frequent patterns are required. The task of mining frequent ....

D. Lin and Z. M. Kedem. Pincer-Search: A new algorithm for discovering the maximum frequent set. In Proc. of the 6th Int'l Conf.on Extending Database Technology (EDBT), pages 105-119, Mar. 1998.

....rules fits in the context of market basket data analysis and highlights a particular feature in customers behavior: 80 of customers who buy cereals and sugar also buy milk. Since the problem was stated [1] various approaches have been proposed for an increased efficiency of rule discovery [2, 4, 8, 17, 23, 24, 26, 30, 33]. However, fully taking advantage of exhibited knowledge means capabilities to handle such a knowledge. In fact, by using a synthetic dataset containing 100,000 objects, each of which encompassing around 10 items, our experiments yield more than 16,000 rules with confidence outcoming 90 . The ....

....Frequent and Frequent Closed Itemsets In Section 4.1, we propose a new algorithm to achieve frequent closed itemsets from frequent itemsets without accessing the dataset. This algorithm discovers frequent closed itemsets while for instance an algorithm for discovering maximal frequent itemsets [4, 17, 33] is used. In Section 4.2, we present an extension of the Apriori algorithm [2] called Apriori Close for discovering frequent and frequent closed itemsets without additional computation time. Like in the Apriori algorithm, we assume in the following that items are sorted in lexicographic order and ....

[Article contains additional citation context not shown here]

D. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. Proc. of the 6th EDBT Conference, pages 105-119, March 1998.

....some look ahead technique in the original Apriori based scheme so that the set of maximum 2Only the exact match of a pattern in the input data is consid ered an occurrence of the pattern. frequent itemsets 3 can be identified without traversal through every frequent itemset. Several algorithms [16, 4, 30] have been proposed along this direction, among which the MaxMiner [4] is the most noted advance. The Max Miner offers simple and effective heuristics to generate candidates for long patterns throughout the mining process and is able to achieve a performance improvement of at least an order of ....

D. Lin and Z. Kedem. Pincer-search: a new algorithm for discovering the maximum frequent set. Proc. 6th Euro. Conf. on Extending Database Technology, 1998.

....support requirement. At each pass, the algorithm determines which candidates are frequent by counting their occurrence. Due to combinatory explosion, this leads to poor performance when frequent pattern sizes are large. To avoid this problem, some algorithms output only maximal frequent patterns [2, 3, 4]. Pincer Search [4] uses a bottom up search along with top down pruning to find maximal frequent patterns. Max Miner [2] uses a heuristic bottom up search to identify frequent sets as early as possible. Even though performance improvements may be substantial, maximal frequent sets have limited use ....

....each pass, the algorithm determines which candidates are frequent by counting their occurrence. Due to combinatory explosion, this leads to poor performance when frequent pattern sizes are large. To avoid this problem, some algorithms output only maximal frequent patterns [2, 3, 4] Pincer Search [4] uses a bottom up search along with top down pruning to find maximal frequent patterns. Max Miner [2] uses a heuristic bottom up search to identify frequent sets as early as possible. Even though performance improvements may be substantial, maximal frequent sets have limited use in association ....

[Article contains additional citation context not shown here]

Lin, D.-I and Kedem, Z. M. 1998. Pincer-Search: A New Algorithm for Discovering the Maximum Frequent Set. In Proc. of the Sixth European Conf. on Extending DatabaseTechnology.

....dense datasets that contain long patterns. Recently, the merits of a depth first approach have been recognized [6] a few algorithms are proposed [2,6,9,12] However, algorithms proposed so far do not fully exploit the strength of depth first search and do not scale to large sparse databases yet. [2,5,6,10] propose algorithms that output only maximal frequent patterns by pruning the frequent item set tree based on superset frequency. However, maximal frequent patterns have limitations in generation of association rules. The representation of projected transaction subsets can be arraybased [12] ....

D-I. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In 6th Intl. Conf. Extending Database Technology, March 1998.

....some look ahead technique in the original Apriori based scheme so that the set of maximum Only the exact match of a pattern in the input data is considered an occurrence of the pattern. frequent itemsets can be identified without traversal through every frequent itemset. Several algorithms [16, 4, 30] have been proposed along this direction, among which the MaxMiner [4] is the most noted advance. The Max Miner offers simple and effective heuristics to generate candidates for long patterns throughout the mining process and is able to achieve a performance improvement of at least an order of ....

D. Lin and Z. Kedem. Pincer-search: a new algorithm for discovering the maximum frequent set. Proc. 6th Euro. Conf. on Extending Database Technology, 1998.

....on the anti monotone Apriori heuristic (see [1] and build frequent sets in a bottom up way, running in time proportional to the number of frequent sets. It was demonstrated recently in [21] that these methods are inadequate in practice when there are (many) frequent sets of large size (see also [4, 39, 44]) due to the fact that the number of frequent sets can be exponentially larger than I(F) Thus these results show that it is perhaps more e#cient to find the boundary of the frequent sets, i.e. the union F # I(F) 17 (proposed e.g. in [64] and use it as a condensed representation of ....

D. Lin and Z.M. Kedem, Pincer-search: a new algorithm for discovering the maximum frequent set, Proc. 6th European Conference on Extending Database Technology, to appear.

....the anti monotone Apriori heuristic (see [1] and build frequent sets in a bottom up 19 way, running in time proportional to the number of frequent sets. It was demonstrated recently in [21] that these methods are inadequate in practice when there are (many) frequent sets of large size (see also [4, 40, 45]) due to the fact that the number of frequent sets can be exponentially larger than I(F) Thus these results show that it is perhaps more e#cient to find the boundary of the frequent sets, i.e. the union F # I(F) proposed e.g. in [66] and use it as a condensed representation of the data ....

D. Lin and Z.M. Kedem (2002). Pincer-search: a new algorithm for discovering the maximum frequent set. em TKDE, 14 (3), 553--566.

....the anti monotone Apriori heuristic (see [2] and build frequent sets in a bottom up way, running in time proportional to the number of frequent sets. It was also demonstrated recently in [9] that these methods are inadequate in practice when there are (many) frequent sets of large size (see also [4, 13, 19]) due the fact that can be exponentially larger than . These results show that it is perhaps more important to find the boundary of the frequent sets, i.e. the families of maximal frequent and minimal infrequent sets t (proposed e.g. in [26] and use those as condensed ....

D. Lin and Z.M. Kedem. Pincer-search: a new algorithm for discovering the maximum frequent set. In: Proceedings of the Sixth European Conference on Extending Database Technology, to appear.

....the antimonotone Apriori heuristic (see [2] and build frequent sets in a bottom up way, running in time proportional to the number of frequent sets. It was also demonstrated recently in [9] that these methods are inadequate in practice when there are (many) frequent sets of large size (see also [4, 13, 20]) due the fact that can be exponentially larger than . These results show that it is perhaps more important to find the boundary of the frequent sets, i.e. the families of maximal frequent and minimal infrequent sets t (proposed e.g. in [27] and use those as a condensed ....

D. Lin and Z.M. Kedem. Pincer-search: a new algorithm for discovering the maximum frequent set. In: Proceedings of the Sixth European Conference on Extending Database Technology, to appear.

....if constant support based frequent pattern discovery algorithms are used to find some of the longer but infrequent patterns, they will end up generating an exponentially large number of short patterns. In the context of the frequent itemset mining, maximal frequent itemset discovery algorithms [4, 7, 2, 13] can potentially 3 be used to find some of these longer itemsets, but these algorithms can still generate a very large number of short infrequent itemsets if these itemsets are maximal. As for the frequent sequential pattern mining, even the problem of finding maximal patterns has not been ....

D.-I. Lin and Z. M. Kedem. Pincer search: A new algorithm for discovering the maximum frequent set. In Extending Database Technology, pages 105--119, 1998.

....if constant support based frequent pattern discovery algorithms are used to find some of the longer but infrequent patterns, they will end up generating an exponentially large number of short patterns. In the context of the frequent itemset mining, maximal frequent itemset discovery algorithms [4, 7, 2, 13] can potentially 3 be used to find some of these longer itemsets, but these algorithms can still generate a very large number of short infrequent itemsets if these itemsets are maximal. As for the frequent sequential pattern mining, even the problem of finding maximal patterns has not been ....

D.-I. Lin and Z. M. Kedem. Pincer search: A new algorithm for discovering the maximum frequent set. In Extending Database Technology, pages 105--119, 1998.

....are small relative to the number of items in the database. That is, we restrict our attention to the class of algorithms that take a bottom up approach to enumerate the solution space consisting of the lattice of all possible itemsets. The problem of mining long patterns has been addressed in [7, 14, 2] and solution techniques for such patterns require a combination of top down and bottom up methods to be viable. 2.5 Mining Algorithms Input Output All online mining algorithms in our study take as input the database D in item list (IL) format and the minimum support threshold minsup and produce ....

D. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In Intl. Conf. on Extending Database Technology, March 1998.

....finding the maximal elements include All MFS [5] which works by iteratively attempting to extend a working pattern until failure. A randomized version of the algorithm that uses vertical bit vectors was studied, but it does not guarantee every maximal pattern will be returned. The Pincer Search [7] algorithm uses horizontal data format. It not only constructs the candidates in a bottom up manner like Apriori, but also starts a topdown search at the same time, maintaining a candidate set of maximal patterns. This can help in reducing the number of database scans, by eliminating non maximal ....

D.-I. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In Intl. Conf. Extending Database Technology, Mar. 1998.

....gain its huge practical relevance. These include the AprioriTid approach for minimizing the number of database passes [2] and sampling approaches for estimating the support of item sets [2, 11] In particular, ecient search for frequent itemsets has been addressed intensely and successfully [7, 3, 14]. Many of these improvements can, and should be, applied to the PredictiveApriori algorithm as well. ....

D. Lin and Z. Kedem. Pincer search: a new algorithm for discovering the maximum frequent set. In Proceedings of the International Conference on Extending Database Technology, 1998.

....and the minimal con dence thresholds. 3 An itemset of size k is called a k itemset. itemsets, all the frequent itemsets are derived and their supports are determined by performing one nal scan of the context. Four algorithms based on this approach were proposed; they are the Pincer Search [LK98], MaxClique and MaxEclat [ZPOL97] and Max Miner [Bay98] algorithms. These algorithms reduce the number of iterations, and thus decrease the number of context scans and the number of CPU operations carried out, compared to levelwise algorithms for extracting frequent itemsets. 2.3 Algorithms for ....

D. Lin and Z. M. Kedem. Pincer-Search : A new algorithm for discovering the maximum frequent set. Proc. EBDT conf., 105-119, March 1998.

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D-I. Lin and Z.M. Kedem, "Pincer-Search: A New Algorithm for Discovering the Maximum Frequent Set," Proc. Sixth Int'l Conf. Extending Database Technology, Mar. 1998.

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Lin, D.-L., and Kedem, Z.M. 1998. Pincer-search: A new algorithm for discovering the maximum frequent set. In 6th Intl. Conf. on Extending Database Technology, pp. 105--119.

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Lin, D-I., Kedem, Z.M.: Pincer Search: A New Algorithm for Discovering the Maximum Frequent Set. In Proc. of the 6th Int'l Conference on Extending Database Technology (EDBT) (1998) 105--119 Valencia

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D-I. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In 6th Intl. Conf. Extending Database Technology, March 1998.

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D.-I. Lin and Z. M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In 6th Intl. Conf. Extending Database Technology, Mar. 1998.

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D.-I. Lin and Z. M. Kedem. Pincer search: A new algorithm for discovering the maximum frequent set. In Extending Database Technology, pages 105--119, 1998.

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D. Lin and Z.M. Kedem. Pincer-search: A new algorithm for discovering the maximum frequent set. In H.-J. Schek, F. Saltor, I. Ramos, and G. Alonso, editors, EDBT, volume 1377 of Lecture Notes in Computer Science, pages 105-119. Springer, 1998.

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