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A new Informative Generic Base of Association Rules
Gh. Gasmi, S. Ben Yahia, E. Mephu Nguifo, and Y. Slimani
PAKDD’05
Advisor: Jia-Ling Koh Speaker: Tsui-Feng Yen
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Outline
IntroductionMathematical backgroundRelated work on generic bases of asso
ciation rules -Work of Bastide et al. -Work of PhanNew generic baseConclusion
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Introduction The problem of the relevance and the usefulness
of extracted association rules is becoming of primary importance, since an overwhelming number of association rules may be derived
In this paper, we introduce a novel generic base of association rules, The novel generic base is sound and informative
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Mathematical backgroundBasic notions -Formal context
A formal context is a triplet K = (O,A,R), where O represents a finite set of objects (or transactions), A is a finite set of attributes and R is a binary relation (i.e., R ⊆ O×A).
Each couple (o, a) ∈R expresses that the
transaction o ∈ O contains the attribute a ∈ A, objects are denoted by numbers and attributes
by letters.
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Mathematical background(conti)Basic notions -Formal context
define two functions: note: 找出現在這幾個 transaction 中 , 所有共同的出現的 ite
m
note: 找有出現 A 這個 itemset 的所有的 transactions -both compound operators of Φand Ψ are closure operators, i
n particular ω = Φ 。 Ψ is a closure operator.
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Mathematical backgroundBasic notions -Frequent closed itemset :
Closed itemset note :沒有其他的 itemset 跟他的 support 一樣且又包含他的
- Formal concept:
- Minimal generator:
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Mathematical background Basic notions
frequent closed itemset
C 、 AC 、 BE 、 BCE 、 ABCE
ex : AC=Φ(Ψ(AC))= Φ(1 、 3 、 5)=AC ,且 sup=3/5 minimal generator
A 、 B 、 C 、 E 、 AB 、 AE 、 BC 、 CE
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Mathematical background Derivation of association rules : -Association rule R is a relation between itemsets of the for
m R : X⇒ (Y-X), in which X and Y are frequent itemsets, and X⊂ Y
- The valid association rules are those whose the strength metric conf(R)= , is greater than or equal to
the minimal threshold of confidence minconf.
-If conf(R)=1 then R is called exact association rule (ER), otherwise it is called approximative association rule (AR).
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Related work The concept of rule redundancy can be consid
ered as follows :
Ex:R1 : A=>CD R: AB=>C
(X1) (Y1) (X) (Y)
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Related work Work of Bastide et al.
In one paper, the couple (GBE,GBA) of generic bases form a sound and informative generic base.
In another ,the authors presented sound inference axioms for both (GBE and GBA) bases, permitting to derive all association rules from generic bases of association rules.
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Related work Work of Bastide et al.
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Work of Phan
Work of Phan
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Work of Phan
For example:
∅ => AC, {A => AC, C=> AC, and A => C}
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Drawbacks of Work of Phan the presented generic base is not informative, i.e., it
may exist a derivable rule for which it is impossible to determine exactly both its support and confidence
For example : the association rule BE=>C is derivable from the generic
rule E=>ABCE. However, it is impossible to derive the exact confidence and support of the derivable rule from the GBPhan generic base.
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New Generic Base : IGB
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New Generic Base : IGB
Proposition 3. The IGB generic base is informative.
proof:
-sufficient to show that it contains all the necessary information to determine the support of an itemset in a derived rule.
-means that we have to be able to reconstitute all closed itemset by concatenation of the premise and the conclusion of a generic rule
.
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New Generic Base : IGB
-The algorithm considers all the discovered frequent closed itemsets. Hence for a given frequent
closed itemset, say c, it tries to find the smallest minimal generator, say gs, associated to frequent closed itemsets subsumed by c and fulfilling the minsup constraint
-Therefore, the algorithm generates the following ge
neric rule gs => c. Since gs⊂ c, then gs∪c=c.
Conclusion: The IGB generic base is informative.
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Conclusion
presented a critical survey of the reported approaches for defining generic bases of association rules.
introduced a novel generic base, which is sound and informative.
provided a set of sound inference axioms for deriving all association rules from the introduced generic base of association rules.