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SLIDE 1

Data Mining: Association Rules

65

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Data Mining: Association Rules

67

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#$$%$

σ&$'≤ σ&$%'(σ&$ ' # σ&$%∪ )%'≥

$$%))%
σ&$∪ )%'≥ σ&$%∪ )'≥

σ&$∪ )'≥ # &$%⇒ )%'≥

&$% ⇒ )'≥

Data Mining: Association Rules 68

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01

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01

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Data Mining: Association Rules 69

* +

2 /- 3

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56

SLIDE 2

Data Mining: Association Rules

71

10

15 20 25 30 35

2 3 5 6 1 1 Timeline Object A: Object B: Object C: 4 5 6 2 7 8 1 2 1 6 1 7 8

Object Timestamp Events A 10 2, 3, 5 A 20 6, 1 A 23 1 B 11 4, 5, 6 B 17 2 B 21 7, 8, 1, 2 B 28 1, 6 C 14 1, 8, 7

Sequence Database:

Data Mining: Association Rules 72

7*/28 *9:*

9:*
2
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7
7

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!"# !$#

%
Data Mining: Association Rules

73

&

* &' <=% > 3?

, &' <0% 31 ,

@AA

*6

&'

Data Mining: Association Rules 74

+

=0"10,10981089 81 0B810.810B1?

B &'+

=0C10///D1?

Data Mining: Association Rules 75

& %

*=% 3? =% 3?&≥ '- %= =3= %⊆ % ⊆ … ⊆

=0 E10 E10>F1? =0% 10>E1? =0 E10>FG10H1? 9 ) =0 10E1? : =0%10 1? ) =0 10>F1? 8 B

/

*

&≥ '

SLIDE 3

Data Mining: Association Rules 76

' 2+

6

/+

C≥

Data Mining: Association Rules 77

' 2+=01010101?

,-+

=01010101?=01?=0101?

"6- 6 =01010101?<I <E+)JJ))JJJ) =010101?

126 4 9 : Answer =         =         k n

Data Mining: Association Rules 78

'

Minsup = 50% Examples of Frequent Subsequences: < {1,2} > s=60% < {2,3} > s=60% < {2,4}> s=80% < {3} {5}> s=80% < {1} {2} > s=80% < {2} {2} > s=60% < {1} {2,3} > s=60% < {2} {2,3} > s=60% < {1,2} {2,3} > s=60% Object Timestamp Events A 1 1,2,4 A 2 2,3 A 3 5 B 1 1,2 B 2 2,3,4 C 1 1, 2 C 2 2,3,4 C 3 2,4,5 D 1 2 D 2 3, 4 D 3 4, 5 E 1 1, 3 E 2 2, 4, 5

Data Mining: Association Rules 79

'( 2+% >3 8%6+

=0%1?=0 1?=0>1?3=01?

8 6+

=0% 1?=0%>1?3=0%10%1?=0%10 1?3=06%101?

8>6+

=0% >1?=0% E1?3=0% 10%1?=0% 10 1?3 =0%10% 1?=0%10%>1?3=0%10%10%1?=0%10%10 1?3

Data Mining: Association Rules 80

)

7&< '+

5%6=0%1?=0 1? 6+=0%10 1?=0% 1?

2&? '+

/&6%'6% 6 %

/

%- # % . %

Data Mining: Association Rules 81

)

5 %<=0%10 >10E1? <=0 >10EF1? =0%10 >10EF1? &EF' 5 %<=0%10 >10E1? <=0 >10E10F1? =0%10 >10E10F1? &EF' % <=0%10 G10E1? <=0%10 10EF1? =0%10 G10EF1? % =0%10 G10F1?

SLIDE 4

Data Mining: Association Rules 82

)*!)#

++

59 %6

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)+

5&6%'

+

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+

59

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Data Mining: Association Rules 83

)

< {1} {2} {3} > < {1} {2 5} > < {1} {5} {3} > < {2} {3} {4} > < {2 5} {3} > < {3} {4} {5} > < {5} {3 4} > < {1} {2} {3} {4} > < {1} {2 5} {3} > < {1} {5} {3 4} > < {2} {3} {4} {5} > < {2 5} {3 4} > < {1} {2 5} {3} >

Frequent 3-sequences Candidate Generation Candidate Pruning

Data Mining: Association Rules 84

$!"# {A B} {C} {D E}

<= ms <= xg >ng

xg: max-gap ng: min-gap ms: maximum span : =0%10E1? =0%10 10>10E10F1? =0% 10>10 >10>E10 E10EF1? =0%10 >10>E10EF1? =0 E10>FG10EK10EF10H1?

:

=0% 10F1? ) =0 10>10F1? ) =0G10F1?

%

xg = 2, ng = 0, ms= 4

Data Mining: Association Rules 85

.$

*%+

5 ;

* +

52B;

L+
9 *

Data Mining: Association Rules 86

Object Timestamp Events A 1 1,2,4 A 2 2,3 A 3 5 B 1 1,2 B 2 2,3,4 C 1 1, 2 C 2 2,3,4 C 3 2,4,5 D 1 2 D 2 3, 4 D 3 4, 5 E 1 1, 3 E 2 2, 4, 5 Suppose: xg = 1 (max-gap) ng = 0 (min-gap) ms = 5 (maximum span) minsup = 60% <{2} {5}> support = 40% but <{2} {3} {5}> support = 60% %% /%

Data Mining: Association Rules 87

%

<=%?= ?3=?

+

% %

>

MM &'

,-+<=0%10 1?

=0%10 >1?=0% 10 10>1?=0>E10% 10 >10E1?
=0%10>10 1?=0 10%10>10 1?

SLIDE 5

Data Mining: Association Rules 88

+

*6 &6%'6

+

*6 &6%'6

Data Mining: Association Rules 89

$!""# {A B} {C} {D E}

<= ms <= xg >ng <= ws

xg: max-gap ng: min-gap ws: window size ms: maximum span =0% 10 >10>E10EF1? =0% >E10F10G1? =0 E10>FG10EK10EG10H1?

)

=0% 10>E1? : =0%E10F1? : =0>10F1?

%

xg = 2, ng = 0, ws = 1, ms= 5

Data Mining: Association Rules 90

2+=01?

* =3013? =3013013?&&01' &01'≤ ' =3013013?&&01' &01'≤ '

Data Mining: Association Rules

91

0&

#

,-+
2
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E1 E2 E1 E2 E1 E2 E3 E4 E3 E4 E1 E2 E2 E4 E3 E5 E2 E3 E5 E1 E2 E3 E1 Pattern: <E1> <E3>