A Generic Algorithm for Generating Closed Sets of a Binary Relation

Gély, Alain

doi:10.1007/978-3-540-32262-7_15

Cited by 13 publications

(18 citation statements)

References 5 publications

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“…We generate candidates by applying the "divide-and-conquer" algorithm published in [2,5,3]. In a nutshell, the algorithm recursively enumerates, in depth-first manner, all itemsets containing an element, say a, and then all itemsets not containing a.…”

Section: Candidate Generationmentioning

confidence: 99%

A new constraint for mining sets in sequences

Čule¹,

Goethals²,

Robardet³

2009

Proceedings of the 2009 SIAM International Conference on Data Mining

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Discovering interesting patterns in event sequences is a popular task in the field of data mining. Most existing methods try to do this based on some measure of cohesion to determine an occurrence of a pattern, and a frequency threshold to determine if the pattern occurs often enough. We introduce a new constraint based on a new interestingness measure combining the cohesion and the frequency of a pattern. For a dataset consisting of a single sequence, the cohesion is measured as the average length of the smallest intervals containing the pattern for each occurrence of its events, and the frequency is measured as the probability of observing an event of that pattern. We present a similar constraint for datasets consisting of multiple sequences. We present algorithms to efficiently identify the thus defined interesting patterns, given a dataset and a user-defined threshold. After applying our method to both synthetic and real-life data, we conclude that it indeed gives intuitive results in a number of applications.

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Section: Candidate Generationmentioning

confidence: 99%

A new constraint for mining sets in sequences

Čule¹,

Goethals²,

Robardet³

2009

Proceedings of the 2009 SIAM International Conference on Data Mining

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“…There are several efficient algorithms listing all closed sets of a closure operator like the divide and conquer algorithm from formal concept analysis [9]. Adapting a closed frequent itemset miner like LCM [16] to our task is even more natural: we plug in optimistic estimate pruning instead of frequency pruning, and instead of single items we have single constraints.…”

Section: Lemma 6 (Pasquier Et Al [14]) the Map σ Is A Closure Operamentioning

confidence: 99%

“…Furthermore, the sorting of the constraint set can have a substantial impact on the computation time. It is, however, a non-trivial problem to find an optimal sorting (see [9] for a comparison of different sorting strategies for divide and conquer closed set listing).…”

Section: Assume That (Ii) Is Violated For Some [H] Then Choose a Clamentioning

confidence: 99%

Non-redundant Subgroup Discovery Using a Closure System

Boley

Großkreutz

2009

Machine Learning and Knowledge Discovery in Databases

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Abstract. Subgroup discovery is a local pattern discovery task, in which descriptions of subpopulations of a database are evaluated against some quality function. As standard quality functions are functions of the described subpopulation, we propose to search for equivalence classes of descriptions with respect to their extension in the database rather than individual descriptions. These equivalence classes have unique maximal representatives forming a closure system. We show that minimum cardinality representatives of each equivalence class can be found during the enumeration process of that closure system without additional cost, while finding a minimum representative of a single equivalence class is NP-hard. With several real-world datasets we demonstrate that search space and output are significantly reduced by considering equivalence classes instead of individual descriptions and that the minimum representatives constitute a family of subgroup descriptions that is of same or better expressive power than those generated by traditional methods.

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“…Given a closure operator there are several listing algorithms (e.g., [3,5]) that enumerate the corresponding closure system using explicit closure computations. They have in common that their listing strategy is efficient, i.e., has polynomial delay, as long as the given closure operator is computed efficiently.…”

Section: Pattern Complexitymentioning

confidence: 99%

“…Among the generic algorithms solving the first task, we have considered the algorithms of Ganter and Reuter [3] and of Gély [5].…”

Section: Integration Into Listingmentioning

confidence: 99%

Efficient Discovery of Interesting Patterns Based on Strong Closedness

Boley

Horváth

Wrobel

2009

Proceedings of the 2009 SIAM International Conference on Data Mining

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Finding patterns that are interesting to a user in a certain application context is one of the central goals of Data Mining research. Regarding all patterns above a certain frequency threshold as interesting is one way of defining interestingness. In this paper, however, we argue that in many applications, a different notion of interestingness is required in order to be able to capture "long", and thus particularly informative, patterns that are correspondingly of low frequency. To identify such patterns, our proposed measure of interestingness is based on the degree or strength of closedness of the patterns. We show that (a) indeed this definition selects long interesting patterns that are difficult to identify with frequency-based approaches, and (b) that it selects patterns that are robust against noise and/or dynamic changes. We prove that the family of interesting patterns proposed here forms a closure system and use the corresponding closure operator to design a mining algorithm listing these patterns in amortized quadratic time. In particular, for non-sparse datasets its time complexity is O(nm) per pattern, where n denotes the number of items and m the size of the database. This is equal to the best known time bound for listing ordinary closed frequent sets, which is a special case of our problem. We also report empirical results with realworld datasets.

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A Generic Algorithm for Generating Closed Sets of a Binary Relation

Cited by 13 publications

References 5 publications

A new constraint for mining sets in sequences

A new constraint for mining sets in sequences

Non-redundant Subgroup Discovery Using a Closure System

Efficient Discovery of Interesting Patterns Based on Strong Closedness

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