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410
Fast algorithms for frequent itemset mining using FPtrees
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 2005
"... Efficient algorithms for mining frequent itemsets are crucial for mining association rules as well as for many other data mining tasks. Methods for mining frequent itemsets have been implemented using a prefixtree structure, known as an FPtree, for storing compressed information about frequent it ..."
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Cited by 64 (0 self)
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Efficient algorithms for mining frequent itemsets are crucial for mining association rules as well as for many other data mining tasks. Methods for mining frequent itemsets have been implemented using a prefixtree structure, known as an FPtree, for storing compressed information about frequent itemsets. Numerous experimental results have demonstrated that these algorithms perform extremely well. In this paper, we present a novel FParray technique that greatly reduces the need to traverse FPtrees, thus obtaining significantly improved performance for FPtreebased algorithms. Our technique works especially well for sparse data sets. Furthermore, we present new algorithms for mining all, maximal, and closed frequent itemsets. Our algorithms use the FPtree data structure in combination with the FParray technique efficiently and incorporate various optimization techniques. We also present experimental results comparing our methods with existing algorithms. The results show that our methods are the fastest for many cases. Even though the algorithms consume much memory when the data sets are sparse, they are still the fastest ones when the minimum support is low. Moreover, they are always among the fastest algorithms and consume less memory than other methods when the data sets are dense.
Association Mining
, 2006
"... The task of finding correlations between items in a dataset, association mining, has received considerable attention over the last decade. This article presents a survey of association mining fundamentals, detailing the evolution of association mining algorithms from the seminal to the stateofthe ..."
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Cited by 61 (1 self)
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The task of finding correlations between items in a dataset, association mining, has received considerable attention over the last decade. This article presents a survey of association mining fundamentals, detailing the evolution of association mining algorithms from the seminal to the stateoftheart. This survey focuses on the fundamental principles of association mining, that is, itemset identification, rule generation, and their generic optimizations.
New Algorithms for Enumerating All Maximal Cliques
, 2004
"... Abstract. In this paper, we consider the problems of generating all maximal (bipartite) cliques in a given (bipartite) graph G = (V, E) with n vertices and m edges. We propose two algorithms for enumerating all maximal cliques. One runs with O(M(n)) time delay and in O(n 2) space and the other runs ..."
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Cited by 60 (1 self)
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Abstract. In this paper, we consider the problems of generating all maximal (bipartite) cliques in a given (bipartite) graph G = (V, E) with n vertices and m edges. We propose two algorithms for enumerating all maximal cliques. One runs with O(M(n)) time delay and in O(n 2) space and the other runs with O( ∆ 4) time delay and in O(n + m) space, where ∆ denotes the maximum degree of G, M(n) denotes the time needed to multiply two n × n matrices, and the latter one requires O(nm) time as a preprocessing. For a given bipartite graph G, we propose three algorithms for enumerating all maximal bipartite cliques. The first algorithm runs with O(M(n)) time delay and in O(n 2) space, which immediately follows from the algorithm for the nonbipartite case. The second one runs with O( ∆ 3) time delay and in O(n + m) space, and the last one runs with O( ∆ 2) time delay and in O(n + m + N∆) space, where N denotes the number of all maximal bipartite cliques in G and both algorithms require O(nm) time as a preprocessing. Our algorithms improve upon all the existing algorithms, when G is either dense or sparse. Furthermore, computational experiments show that our algorithms for sparse graphs have significantly good performance for graphs which are generated randomly and appear in realworld problems. 1
Depthfirst nonderivable itemset mining
 In SIAM Int. Conf. on Data Mining (SDM’05
, 2005
"... Mining frequent itemsets is one of the main problems in data mining. Much effort went into developing efficient and scalable algorithms for this problem. When the support threshold is set too low, however, or the data is highly correlated, the number of frequent itemsets can become too large, indepe ..."
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Cited by 58 (7 self)
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Mining frequent itemsets is one of the main problems in data mining. Much effort went into developing efficient and scalable algorithms for this problem. When the support threshold is set too low, however, or the data is highly correlated, the number of frequent itemsets can become too large, independently of the algorithm used. Therefore, it is often more interesting to mine a reduced collection of interesting itemsets, i.e., a condensed representation. Recently, in this context, the nonderivable itemsets were proposed as an important class of itemsets. An itemset is called derivable when its support is completely determined by the support of its subsets. As such, derivable itemsets represent redundant information and can be pruned from the collection of frequent itemsets. It was shown both theoretically and experimentally that the collection of nonderivable frequent itemsets is in general much smaller than the complete set of frequent itemsets. A breadthfirst, Aprioribased algorithm, called NDI, to find all nonderivable itemsets was proposed. In this paper we present a depthfirst algorithm, dfNDI, that is based on Eclat for mining the nonderivable itemsets. dfNDI is evaluated on reallife datasets, and experiments show that dfNDI outperforms NDI with an order of magnitude. 1
Generating a condensed representation for association rules
 JOURNAL OF INTELLIGENT INFORMATION SYSTEMS, KLUWER ACADEMIC PUBLISHER
, 2005
"... Association rule extraction from operational datasets often produces several tens of thousands, and even millions, of association rules. Moreover, many of these rules are redundant and thus useless. Using a semantic based on the closure of the Galois connection, we define a condensed representation ..."
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Cited by 49 (6 self)
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Association rule extraction from operational datasets often produces several tens of thousands, and even millions, of association rules. Moreover, many of these rules are redundant and thus useless. Using a semantic based on the closure of the Galois connection, we define a condensed representation for association rules. This representation is characterized by frequent closed itemsets and their generators. It contains the nonredundant association rules having minimal antecedent and maximal consequent, called minmax association rules. We think that these rules are the most relevant since they are the most general nonredundant association rules. Furthermore, this representation is a basis, i.e., a generating set for all association rules, their supports and their confidences, and all of them can be retrieved needless accessing the data. We introduce algorithms for extracting this basis and for reconstructing all association rules. Results of experiments carried out on real datasets show the usefulness of this approach. In order to generate this basis when an algorithm for extracting frequent itemsets—such as APRIORI for instance—is used, we also present an algorithm for deriving frequent closed itemsets and their generators from frequent itemsets without using the dataset.
On the Complexity of Generating Maximal Frequent and Minimal Infrequent Sets
, 2002
"... Let A be an mn binary matrix, t . . . , m} be a threshold, and # > 0 be a positive parameter. We show that given a family of O(n ) maximal tfrequent column sets for A, it is NPcomplete to decide whether A has any further maximal tfrequent sets, or not, even when the number of such ad ..."
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Cited by 47 (11 self)
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Let A be an mn binary matrix, t . . . , m} be a threshold, and # > 0 be a positive parameter. We show that given a family of O(n ) maximal tfrequent column sets for A, it is NPcomplete to decide whether A has any further maximal tfrequent sets, or not, even when the number of such additional maximal tfrequent column sets may be exponentially large. In contrast, all minimal tinfrequent sets of columns of A can be enumerated in incremental quasipolynomial time. The proof of the latter result follows from the inequality # t + 1)#, where # and # are respectively the numbers of all maximal tfrequent and all minimal tinfrequent sets of columns of the matrix A. We also discuss the complexity of generating all closed tfrequent column sets for a given binary matrix.
Mining topk covering rule groups for gene expression data
 In the 24th ACM SIGMOD International Conference on Management of Data
, 2005
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A systematic approach to the assessment of fuzzy association rules. Data Mining and Knowledge Discovery
, 2006
"... In order to allow for the analysis of data sets including numerical attributes, several generalizations of association rule mining based on fuzzy sets have been proposed in the literature. While the formal specification of fuzzy associations is more or less straightforward, the assessment of such ru ..."
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Cited by 43 (6 self)
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In order to allow for the analysis of data sets including numerical attributes, several generalizations of association rule mining based on fuzzy sets have been proposed in the literature. While the formal specification of fuzzy associations is more or less straightforward, the assessment of such rules by means of appropriate quality measures is less obvious. Particularly, it assumes an understanding of the semantic meaning of a fuzzy rule. This aspect has been ignored by most existing proposals, which must therefore be considered as adhoc to some extent. In this paper, we develop a systematic approach to the assessment of fuzzy association rules. To this end, we proceed from the idea of partitioning the data stored in a database into examples of a given rule, counterexamples, and irrelevant data. Evaluation measures are then derived from the cardinalities of the corresponding subsets. The problem of finding a proper partition has a rather obvious solution for standard association rules but becomes less trivial in the fuzzy case. Our results not only provide a sound justification for commonly used measures but also suggest a means for constructing meaningful alternatives. 1.
An efficient algorithm for enumerating closed patterns in transaction databases
 In Proc. DS’04, LNAI 3245
, 2004
"... Abstract: The class of closed patterns is a well known condensed representations of frequent patterns, and have recently attracted considerable interest. In this paper, we propose an efficient algorithm LCM (Linear time Closed pattern Miner) for mining frequent closed patterns from large transaction ..."
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Cited by 42 (11 self)
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Abstract: The class of closed patterns is a well known condensed representations of frequent patterns, and have recently attracted considerable interest. In this paper, we propose an efficient algorithm LCM (Linear time Closed pattern Miner) for mining frequent closed patterns from large transaction databases. The main theoretical contribution is our proposed prefixpreserving closure extension of closed patterns, which enables us to search all frequent closed patterns in a depthfirst manner, in linear time for the number of frequent closed patterns. Our algorithm do not need any storage space for the previously obtained patterns, while the existing algorithms needs it. Performance comparisons of LCM with straightforward algorithms demonstrate the advantages of our prefixpreserving closure extension. 1
LCM ver. 2: Efficient Mining Algorithms for Frequent/Closed/Maximal Itemsets
"... For a transaction database, a frequent itemset is an itemset included in at least a specified number of transactions. A frequent itemset P is maximal if P is included in no other frequent itemset, and closed if P is included in no other itemset included in the exactly same transactions as P. The p ..."
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Cited by 41 (2 self)
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For a transaction database, a frequent itemset is an itemset included in at least a specified number of transactions. A frequent itemset P is maximal if P is included in no other frequent itemset, and closed if P is included in no other itemset included in the exactly same transactions as P. The problems of finding these frequent itemsets are fundamental in data mining, and from the applications, fast implementations for solving the problems are needed. In this paper, we propose efficient algorithms LCM (Linear time Closed itemset Miner), LCMfreq and LCMmax for these problems. We show the efficiency of our algorithms by computational experiments compared with existing algorithms.