A Sliding Window Method for Finding A Sliding Window Method for Finding Recently Frequent Itemsets over OnliRecently Frequent Itemsets over Online Data Streamsne Data StreamsJoong Hyuk Chang and won Suk Lee, Proc. of the 9’th Joong Hyuk Chang and won Suk Lee, Proc. of the 9’th ACM SIGKDD International Conference on Knowledge DACM SIGKDD International Conference on Knowledge Discovery and Data Mining (SIGKDD’03)iscovery and Data Mining (SIGKDD’03)

Adviser: Jia-Ling Koh Speaker: Yu-ting Kung

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Introduction• Most of mining algorithms or

frequency approximation algorithm for a data stream don’t able to extract the recent change of information in a data stream adaptively.

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Introduction (Cont.)• In this paper,

– Propose a sliding window method of finding recently frequent itemsets over an online data stream

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Sliding Window Method• Idea:

– Define significant itemset:• An itemset whose current support is greater than or equal to an error parameter is a significant itemset

– Monitoring only significant itemsets

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SW Method (Cont.)• Two different phases

– Window initialization phase:• Actives while the number of transactions generated so far in a data stream is less than or equal to a predefined window size.• Insert new transaction in CTL (current transaction list)• No extracted transation

– Window sliding phase:• Actives after the CTL becomes full• Insert new transaction in CTL (current transaction list)• The oldest transaction is extracted from the CTL

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SW Method (Cont.)• Five steps:

1. Appending a transaction2. Counting updating and insertion of new itemsets3. Extracting a transaction4. Pruning of itemsets5. Frequent itemset selection

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Step1: Appending a transaction• Content

– The transaction Tk is appended to the current transaction list CTL

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Step2: Counting updating and insertion of new itemsets• Content

– For an itemset e that appears in the Tk with an entry (e, f, t):f: count of the itemset t: TID which makes the itemset be newly inserted into the monitoring lattice

Case 1 its corresponding node is in the monitoring lattice: e.f = e.f + 1Case 2 its corresponding node isn’t in the monitoring lattice: e is inserted into the monitoring lattice with (e, 1, k)

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Step3: Extracting a transaction• When this step is done?

– Only in the window sliding phase• Content

– Extract the oldest transaction in CTL– Update the entry (e, f, t) of this node in the

monitoring lattice:If t <= wfirst e.f = e.f -1;

Wfirst : the TID of the first transaction of the current windowElse e.f = e.f;

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Step4: Pruning of itemsets• Therom:

– Given an error parameter , the maximum possible count of an itemset with its entry (e, f, t) is found as follows:

otherwisewtf

feC

firstk )(

w t if )( firstmax

)(max eCk

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Step4: Pruning of itemsets• When this step is done?

– Periodically or when it is needed• Content

– For an itemset e with entry (e, f, t) in the monitoring lattice: If , Then it can be regarded as an insignificant itemset Prune it !!

k

wk DeC )(max

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Step5: Frequent itemset selection• When this step is done?

– The up-to-date set of recently frequent itemsets is requested.• Content

– For an itemset e with an entry (e, f, t) in the monitoring lattice:If its , min

max )( SDeCk

wk

it is a frequent itemset !!

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For Example• Data Stream

Tid 1

Items

AB

(a) D1

Tid 1 2 3 4 5

Items

AB

D AB

AB

A

(b) D5

Tid 1 2 3 4 5 6 7 8 9 10

Items

AB

D AB

AB

A AC

AE

AC

E AE

(c) D10

Tid 1 2 3 4 5 6 7 8 9 10

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Items

AB

D AB

AB

A AC

AE

AC

E AE

AD

(d) D11

Tid 1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

Items

AB

D AB

AB

A AC

AE

AC

E AE

AD

B A B A

(e) D15

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For Example (Cont.)• Initial value

– Smin = 0.5– = 0.25 (0.5 x Smin) – Window size = 10– Step4 is performed in every 5 transactions.

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e f t

AB

AB

111

111

(a) After T1 (AB)

Step1,2 Step1,2

e f t

AB

ABD

1111

1112

(b) After T2 (D)

Step1,2e f t

AB

ABD

2221

1112

(b.1) After T3 (AB)

Step1,2

(b.2) After T4 (AB)

Step1,2

(b.3) After T5 (A)

Step4

(b.3) After prning

D is pruned from the monitoring lattice, becasueStep1,2 recursively

(C) After T10 (AE)

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e f t

ABCDE

ABACAEAD

932133221

11611716711

Step1,2 Step3

(d) After T11 (AD)

Step4

Step1,2,3,4

(e) After Step4 for T15

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Experiment Result• Data souce

– T5.I4.D1000K-I– T5.I4.D1000K-II

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Experiment (Cont.)• Memory usage in the window

sliding phase

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Experiment (Cont.)• Average support error

– Measure the relative accuracy of the proposed method

– When two sets of mining results

and are given for the same data set, the average support error ASE(R2|R1) is defined:

1

2121

1221221211

)(|})()({|)()|(

R

eSeSeSeSRRASE RRRe

mRRe

mmRRRe

mmmm

})(|))(,{( min111 SeSeSeR iii

})(|))(,{( min222222 SeSeSeR

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Experiment (Cont.)• Average support error of the mining result of the proposed method with respect to that of the Apriori algorithm on the transactions within the current window

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Experiment (Cont.)• The average processing time(Step1-

Step4) of the sliding window method in each interval

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Experiment (Cont.)• The average processing time for

Step5

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Experiment (Cont.)• The memory usage of the window

sliding phase by varying the size of the window

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Experiment (Cont.)• The average processing time of

the sliding window method by varying the size of a window

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Conclusion• The result of the proposed method guarantees the following:

– All itemsets whose true supports are greater than or equal to a minimum support Smin are found– No itemset whose true support is less than (Smin- ) is found as a recently frequent itemset – For each itemeset, the difference between its estimated support and its true support is less than