CloSpan: Mining Closed Sequential Patterns in Large Datasets

CloSpan: Mining Closed Sequential Patterns in Large Datasets. PowerPoint Presentation CloSpan Mining Closed Sequential Patterns in Large Datasets SEQUENTIAL PATTERNS Natural Language Processing Lab , NTU, 2006 Slide Outline Introduction Search Space Pruning Cl.

CloSpan: Mining Closed

Sequential Patterns in Large

Datasets SEQUENTIAL PATTERNS

element are listed alphabetically

<a(bc)dc> is a

subsequence of <a(abc) (ac)d(cf)>

Given support threshold min_sup_count =2, <(ab)c> is a

Introduction (Cont.)

 Definition

– Frequent Sequential Pattern (FS)

Include all the sequences whose support is no less than

min_sup

– Closed Frequent Sequential Pattern (CS)

Include no sequence which has a super-sequence with the same support

CS  FS

Introduction (Cont.)

 Example – FS & CS

(af)dea eab

e(abf)(bde)

0 1 2

ea:3, (af)d:2, (af)e:2, eab:2

Introduction (Cont.)

 Definition

– Prefix and Postfix (Projection)

 <a>, <aa>, <a(ab)> and <a(abc)>

(ac)d(cf)>

 Given sequence <a(abc)(ac)d(cf)>

Prefix Postfix /Projection

<a> <(abc)(ac)d(cf)>

<aa> <(_bc)(ac)d(cf)>

<ab> <(_c)(ac)d(cf)>

 Ex: s=<(ed)a> và  ={e} thì <(ed)(ae)> is

an I-Step extension of <(ed)a>

– S-Step extension

 s s  = <e 1 , e 2 , …, e m , {}>

 Ex: <(a)(e)> is an S-Step extension of <(a)>

Search Space Pruning (Cont.)

 Definition

 Total number of items in D

 Two sequences s and s’, s  s’

 Ds = D s’  (Ds) = (Ds’)

 Example

– D f = D (af) = {de, (de)}

 (D(af)) = (Df) = 4

Search Space Pruning (Cont.)

 Definition

 Two sequences s and s’, s  s’

Search Space Pruning (Cont.)

f

Search Space Pruning (Cont.)

Search Space Pruning (Cont.)

 CloSpan( s , D s , min_sup, L)

– Input: A sequence s, a projectd DB D s , and min_sup

– Output: The prefix search lattice L

– Check whether a discovered sequence s’ exist s.t either s  s’ or s’  s,

and (D s ) = (D s’ );

– if such super-pattern or sub-pattern exists then

 Modify the link in L, return;

– else insert s into L;

– scan D s once, find every frequent item  such that

 s can be extended to (s  i ), or

 s can be extended to (s s );

– if no valid  available then

 return;

– for each valid  do  I-Step

 Call CloSpan(s i  , D s  i  , min_sup , L );

– for each valid  do  S-Step

 Call CloSpan(s s  , D s s  , min_sup , L );

– return;

CloSpan (Cont.)

 Example

(af)dea eab

e(abf)(bde)

0 1 2

min_sup_count = 2

a:3, b:2, d:2, e:3, f:2

0 1 2

nil nil nil

CloSpan (Cont.)

 Example (Cont.)

<>

0 1 2 3

a s :3

4

f i :2

0 1 2 3

0 1 2

0 1 2

e s :3

nil

e s :3

nil

a s :3

nil

e s :3

nil

a s :3

nil

Experimental Results

 Synthetic Data

– Parameters

 D : Number of sequences in 000s

 C : Average itemsets per sequence

 T : Average items per itemset

 N : Number of different items in 000s

 S : Average itemsets in maximal sequences

 I : Average items in maximal sequences

– Two Data Set

 D10 C10 T2.5 N10 S6 I2.5

 D5 C20 T20 N10 S20 I20

 Real world datasets

– KDDCup2000 – Gazelle Click Stream

Experimental Results (Cont.)

 Synthetic Data

 D10 C10 T2.5 N10 S6 I2.5

Experimental Results (Cont.)

 Synthetic Data

 D5 C20 T20 N10 S20 I20

Experimental Results (Cont.)

 Real world datasets

– KDDCup2000

 29,369 sequences

 35,722 sessions

 87,546 page views

 The average number of sessions in a sequence is around 1

 The average number of pageviews in a session is 2

 The largest session contains 342 views

 The longest sequence has 140 sessions

 The largest sequence contains 651 page views

Experimental Results (Cont.)

 Clospan to mine frequent closed sequences efficiently.

 Clospan outperforms PrefixSpan.

Lexicographic Sequence Tree

 Definition

– Lexicographic Sequence Tree

<>

<(a)> <(b)>

<(ab)> <(a)(a)> <(a)(b)>

<(ab)(a)> <(ab)(b)> <(a)(bc)> <(a)(bd)>

Search Space Pruning

 Definition

 a subsequence s, projected database Ds

 if ,  is a common prefix for all the sequence with the same extension type (either itemset-extension or

sequence-extension) in Ds

 , if s   is closed,  must be a prefix of 

 , we need not search s   and its descendants except the branch of s  

 Example

– D s = {de(af), de(fg)}

– s  <de> not closed  unnecessary to extend s  <e>

Search Space Pruning (Cont.)

Search Space Pruning (Cont.)

– Partial Order

D s        = D s