Mining All Non-derivable Frequent Itemsets

Calders, Toon; Goethals, Bart

doi:10.1007/3-540-45681-3_7

Cited by 205 publications

(200 citation statements)

References 13 publications

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“…A disjunction-free set is an itemset I where there do not exist i 1 and i 2 with supp(I) = supp(I \ {i 1 2 The frequent disjunction-free sets together with their support and the minimal non-frequent ones allow to compute the support of all frequent itemsets. This approach is further extended in [16] to non-derivable itemsets, where the previous equation is extended from the two elements i 1 and i 2 to an arbitrary number of elements.…”

Section: History and State Of The Art In Fca-based Association Rule Mmentioning

confidence: 99%

“…In [22], the non-derivable itemsets [16] as described above are used to define a set of non-derivable association rules. This set is a lossless subset of the minmax basis, but the reduction comes with the cost of more complex formulae for computing support and confidence of the derivable rules by determining upper and lower bounds, based on set inclusion-exclusion principles.…”

Section: Bases Of Association Rulesmentioning

confidence: 99%

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Efficient Mining of Association Rules Based on Formal Concept Analysis

Lakhal

Stumme

2005

Formal Concept Analysis

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Abstract. Association rules are a popular knowledge discovery technique for warehouse basket analysis. They indicate which items of the warehouse are frequently bought together. The problem of association rule mining has first been stated in 1993. Five years later, several research groups discovered that this problem has a strong connection to Formal Concept Analysis (FCA). In this survey, we will first introduce some basic ideas of this connection along a specific algorithm, Titanic, and show how FCA helps in reducing the number of resulting rules without loss of information, before giving a general overview over the history and state of the art of applying FCA for association rule mining.

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Section: History and State Of The Art In Fca-based Association Rule Mmentioning

confidence: 99%

Section: Bases Of Association Rulesmentioning

confidence: 99%

Efficient Mining of Association Rules Based on Formal Concept Analysis

Lakhal

Stumme

2005

Formal Concept Analysis

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“…[2][3][4][5][6][7][8][9][10][11]Implementation of an algorithm which mines high utility itemsets from the given dataset must be focused on minimum memory usage as well as the time required to execute the main task. The CHUD algorithm works in bottom up manner.…”

Section: Introductionmentioning

confidence: 99%

Optimal Implementation of CHUD based on Association Matrix

Dhande¹,

Patil²

2014

International Journal of Advanced Research in Computer and Comm

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An implementation always has different set of issues, though we have an algorithm or any sort of blueprint ready to solve the problem. This paper describes how CHUD [1] is implemented in C#.Net. Overall four to five main modules we have to form, namely, Connection Module, CHUD Module, DAHU [1] Module, Dataset Population Module and Result Analysis module. Each of the modules has its own significance and contribution. The Connection Module allows us to connect our software to our database file CHUD.accdb as well as to the dataset on which utility mining should be performed. This module will collect the information about columns like ItemSold (which actually contains the itemnames/itemids sold in transaction), transaction Id, item quantity, profit unit etc. As we know CHUD works on promising items only, we need to extract promising items from the given dataset. At the same time while we scan whole dataset we build an association matrix/table which is a vertical representation of given dataset. CHUD module discovers closed high utility itemsets, and records these itemsets in PhaseIOutput table in CHUD.mdb. DAHU later on uses each itemset from PhaseIOutput table and work from the top. Work from the top suggest that it operates on the itemsets of maximum length "k" and discovers all possible high utility itemsets of length "k-1", which not present in PhaseIOutput table. All high utility itemsets discovered by DAHU recorded in PhaseIIOutput. The both the tables PhaseIOutput and PhaseIIOutput combinely form a final result set which have all the high utility itemsets for the given dataset. C= {X1, X2………...Xn} where Xi ∈PhaseIOutput. D= {Y1, Y2………. Ym} where Yi ∈PhaseIIOutput. Suppose R is the final result set, then, R=C ∪ D Finally, we represent the result with result pattern module, which use the data of both the table PhaseIOutput and PhaseIIOutput, and represent the items and itemsets with their utility value in Bar chart, PI Chart or any other representation style element. One can make a good analysis with these results.

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“…The best-known example of a condensed representation is the closed itemsets representation [14]. Other examples are the Free Sets [2], the Disjunction Free Sets [3], the Generalized Disjunction Free Sets [12], and the Non-Derivable Sets [7].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Bounds on the Size of Condensed Representations

Dexters

Calders

2005

Lecture Notes in Computer Science

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Abstract. Recent studies demonstrate the usefulness of condensed representations as a semantic compression technique for the frequent itemsets. Especially in inductive databases, condensed representations are a useful tool as an intermediate format to support exploration of the itemset space. In this paper we establish theoretical upper bounds on the maximal size of an itemset in different condensed representations. A central notion in the development of the bounds are the l-free sets, that form the basis of many well-known representations. We will bound the maximal cardinality of an l-free set based on the size of the database. More concrete, we compute a lower bound for the size of the database in terms of the size of the l-free set, and when the database size is smaller than this lower bound, we know that the set cannot be l-free. An efficient method for calculating the exact value of the bound, based on combinatorial identities of partial row sums, is presented.

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Mining All Non-derivable Frequent Itemsets

Cited by 205 publications

References 13 publications

Efficient Mining of Association Rules Based on Formal Concept Analysis

Efficient Mining of Association Rules Based on Formal Concept Analysis

Optimal Implementation of CHUD based on Association Matrix

Theoretical Bounds on the Size of Condensed Representations

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