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Finding Recent Frequent ItemsetFinding Recent Frequent Itemsets Adaptively over Online Data Strs Adaptively over Online Data Streamseams

J. H, Chang and W.S. Lee, in Proc. Of the 9th ACM J. H, Chang and W.S. Lee, in Proc. Of the 9th ACM International Conference on Knowledge DiscoverInternational Conference on Knowledge Discovery and Data Ming, 2003.y and Data Ming, 2003.

Adviser: Jia-Ling KohAdviser: Jia-Ling KohSpeaker: Shu-Ning ShinSpeaker: Shu-Ning ShinDate: 2004.8.12Date: 2004.8.12

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IntroductionIntroduction• This paper proposes a method of finding recen

t frequent itemsets ：– Significant itemsets are maintained by a prefix-tree

lattice structure called monitoring lattice.– Decaying the old occurrence count of each itemset

as time goes by.– Minimize the number of significant itemsets ：

• delayed-insertion• pruning operations

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Preliminaries (1)Preliminaries (1)• Data Stream can be defined ：

– I={i1, i2, …, in} ： a set of current items.– e ： itemset, a set of item.– Tid ： transaction id, Tk generate at the kth turn.– Dk=<T1, T2, …, Tk>, When new transaction Dk is gener

ated.– |D|k ： the number of transactions in Dk.– Ck(e) ： the number of transactions in Dk that contai

n the itemset e.– Sk(e) ： Support of itemset e in Dk.

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Preliminaries (2)Preliminaries (2)• Decay rate： the reducing rate of a

weight for a fixed decay-unit.• d=b-(1/h), (b>1, h≧1, b-1≦d<1)

– decay-unit： the chunk of information to be decayed together.

– decay-base b： the amount of weight reduction per a decay-unit and greater than 1.

– decay-base-life h： defined by the number of decay-units that makes the current weight be b-1.

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Preliminaries (3)Preliminaries (3)• The total number of transactions |D|k in the cur

rent data stream Dk ：

– The value of |D|k converges to 1/(1-d) as the value k increases infinitely.

• The count Ck(e) of an itemset e in the current data stream Dk ：

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Count Estimation of Count Estimation of an itemset (1)an itemset (1)

• The maximum possible count of an itemset is estimated by the minimum value among the maximum possible counts of all of its subsets.

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Count Estimation of Count Estimation of an itemset (2)an itemset (2)

• Definition 1 ：– ： a set of itemset e’s subsets– ： a set of e’s m-subsets– ： a set of counts for e’s m-subsets

• Definition 2 ：– Union-itemset is composed of all items that are

members of either e1 or e2.– Intersection-itemset is composed of all items th

at are members of both e1 and e2.

)(ePCm

)(ePm

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21 ee

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• exclusively distributed (LED) ： the items of an itemset appear together in as many transactions as possible.

• most exclusively distributed (MED) ： the items of an itemset appear exclusively as many transactions as possible.

• The maximum count of n-itemset e ：

Count Estimation of Count Estimation of an itemset (3)an itemset (3)

))(min()( 1max ePeC C

n

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Count Estimation of Count Estimation of an itemset (4)an itemset (4)

• Two itemsets e1, e2 ：

• The minimum count of Cmin(e) can be estimated by (n-1)-subset union ：

• Estimation error ：– E(e)=Cmax(e)-Cmin(e)

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estDecestDec Method (1) Method (1)• Every node in a monitoring lattice mainta

ins a triple (cnt, err, MRtid) for its corresponding itemset e ：– cnt ： count of e.– err ： maximum error count of e– Mrtid ： the most recent transacrion id that

contain e

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estDecestDec Method (2) Method (2)• estDec Method is composed of four phas

e ：– Phase Ⅰ ： parameter updating phase– Phase Ⅱ ： count updating phase– Phase Ⅲ ： Delayed insertion phase– Phase Ⅳ ： frequent itemset selection phas

e

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estDecestDec Method (3) Method (3)

• Phase II ： the counts of those itemsets in ML that appear in Tk are updated.– Sprn ： threshold for pruning.– If a 1-itemset is pruned from ML, it is impossible to estimate it

s count later.

Phase I： |D|k is updated.

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estDecestDec Method (4) Method (4)

• Phase III ： Find new itemset that has high possibility to become frequent. Two cases insert new itemset to a ML ：– new 1-itemset, the cnt of 1-itemset is actual.– Itemset e Cmax(e)/|D|k ≧ Sins, Sins ： threshold for delayed-inser

tion.• cntt_for_subsets=(1-d|e|-1)/(1-d)• max_xnt_before_subsets=Sins*(|D|k-(|e|-1))*d|e|-1)• Cupper(e)=Max_xnt_before_subsets+ Cntt_for_subsets

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estDecestDec Method (5) Method (5)

• Phase IV ： produces all current frequent itemsets in ML.– itemset e is frequent if its current support

(cnt * d(k-MRtid))/|D|k is greater than Smin– its current support error ：

• (err*d(k-MRtid))/|D|k

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estDecestDec Method (6) Method (6)• Force-pruning operation ：

– all insignificant itemsets in ML can be pruned

– perform when the current size of ML reaches a threshold.

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Experimental (1)Experimental (1)• Performance of the estDec method for the data set T10.

I4.D1000K– Sins is denoted p%, the actual value=Smin*p%.– Force-pruning operation perform in every 1,000 transactions.– (a) memory usage (b) performance time of Phases I~III (c) perfo

rmance time of Phases IV

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Experimental (2)Experimental (2)• Accuracy of mining result

– Average support error

• ASE(RestDec|RdApriori)

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Experimental (3)Experimental (3)• The adaptability of the estDec method for the chang

e of information in a data stream.– Coverage rate CR(X)

• |R| ： total nmber of frequent itemdets in ML