seqstream: mining closed sequential pattern over stream sliding windows lei chang tengjiao wang...

SeqStream: Mining Closed Sequential Pattern over Stream Sliding WindowsSeqStream: Mining Closed Sequential Pattern over Stream Sliding Windows

Lei Chang Tengjiao Wang Dongqing Yang Hua Luan

ICDM’08

Lei Chang Tengjiao Wang Dongqing Yang Hua Luan

ICDM’08

112/04/21 1

Outline.

Preliminary.

Algorithm.

Experimental results.

Conclusion.

112/04/21 2

Preliminary.

The inverse sequence of a sequence s, denoted by s’

s = <abae>, s’= <eaba>

An s-projected database Ds

-projected database is {<da>,<ae>,<cda>,<cdae>,<cda>}

The size of Ds denoted as R(Ds)

The size of -projected database is 14.112/04/21 3

<e>-projected database is {φ,φ,<bcda>,<ac>}

The size of <e>-projected database is 6.

The inverse database of D, denoted by D’

The database in current sliding window after inserting(but before removing), denoted by D^.

D^ : {<fbda>,<abaec>,<fbcdac>,<bcdae>,<ebcdaf>,<aeac>}112/04/21 4

In the inverse database of D^, the set of sequence from user appear in current window is called an insertion database denoted by D+.

The set of sequence from user that appear in remove winodw is called a removal database denoted by D-.

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D^ : {<fbda>,<abaec>,<fbcdac>,<bcdae>,<ebcdaf>,<aeac>}

D^’: {<adbf>,<ceaba>,<cadcbf>,<eadcb>,<fadcbe>,<caea>}

D+ : {<ceaba>,<cadcbf>,<fadcbe>}

D- : {<cadcbf>,<eadcb>,<fadcbe>}

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closed pattern : {<a>:6,<ae>:3,<c>:4,<ba>:5,<bda>:4,

<bcda>:3,<e>:4}

closed pattern : {<a>:6,<ab>:5,<adb>:4,<adcb>:3,<c>:4,

<e>:4,<ea>:3}

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sn : A node n of an IST corresponds a sequence that starts from the root

node to that node, and the sequence is denoted by Sn.

c-node : If sn is a closed sequential sequence in D’, n is a c-node.

t-node : If sn is not a closed sequential sequence in D’ and it does not

have any t-node ancestor.

i-node : n is neither a c-node nor t-node. 112/04/21 9

Algorithm.

Element insertion

Element removal

State update

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Element insertion

Theorem 2 : If a depth-1 node whose item does not occur in the newly coming element, nodes under that node will not change their attribute values and any t-node under it does not change its type after inserting the element.

Theorem 3 : After inserting a new element, if the PDBSize and support of a t-node do not change, it will keep to be a t-node.

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Dc^’ : {<eaba>,<adbf>,,<be>,<aea>}

Df^’ : {φ, φ,<adcbe>}

c : {<eaba>,<ab>,,<be>,<aea>}

ca : {<ba>,,<ea>}

cb : {<a>, φ,<e>}

ce : {<aba>, φ,<a>}

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Element removal

Theorem 5 : After the removal of etc−w, a t-node may be deleted, but it never changes to a c-node or an i-node.

For each child node t of n, it computes st-projected database in the removal database D−

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D − : {<cadcbf>,<eadcb>,<fadcbe>}

Da−: {<dcbf>,<dcb>,<dcbe>}

Db−: {<f> ,φ,<e>}

Dc − : {<adbf>, ,<be>}

……

Df − : {φ,<adcbe>}

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State update

Theorem 6 : Given a t-node n in an IST for the inverse database D, there must exist an i-node or a c-node t in the IST.

i-node => c-node

c-node => t-node

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Experimental results.

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Conclusion.

This paper has proposed a Seqstream algorithm to mine closed sequential pattern in sliding window.

Designed for multi-stream?

112/04/21 20

seqstream: mining closed sequential pattern over stream sliding windows lei chang tengjiao wang...

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