CSE 980: Data Mining

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CSE 980 Data Mining

• Lecture 12 Extension to Association Analysis
  Formulation

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Mining Infrequent Patterns

• An infrequent pattern is an itemset or rule whose
  support is less than minsup threshold
• When do infrequent patterns become interesting?
• Negative correlation
• P(A,B) ltlt P(A)P(B)
• e.g Windows vs Linux
• Exception rules
• (FireYes) ? (AlarmOff) may be infrequent, it is
  interesting because it may suggest a faulty alarm
  system
• Challenge
• There is an enormous number of infrequent patterns

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Negative Associations

• A negative itemset X is an itemset that satisfies
  the following properties
• X A ? B where A is a set of positive items and
  B is a set of negative items
• Support, s(X) minsup
• A negative association rule r is a rule extracted
  from a negative itemset X and satisfies the
  following properties
• S(X) minsup
• Confidence(r) minconf
• Example tea ? coffee

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Negative vs Frequent Patterns
Venn diagram includes all possible patterns
extracted from a given itemset Negative patterns
are either negative itemsets or negative
association rules
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Negative vs Frequent Patterns
minsup 40 minconf 50

• Coke ? Milk (support40, conf 100)
• ? frequent and strong association rule
• Beer ? Milk (support40 conf 67, but
  support(Milk)80)
• ?negatively-correlated pattern
• Milk ? Eggs (support 80, conf
  100)
• ? negative association rule

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Approach 1 Using Negative Items

• Computationally expensive
• Tends to produce many uninteresting negative
  associations

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Approach 1 Using Negative Items
Size 3
B
Size 2
B
A
A
Support of A,B, A,B and A,B can be very
large
C
C
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Approach 2 Using Positive Itemsets

• Boulicaut et al 2000
• Compute support of negative itemsets based on the
  support of positive itemsets
• e.g. X Y ? Z
• e.g. s(ABCD) s(AB)-s(ABC)-s(ABD)s(ABCD)
• To use this formula
• Need to use a very low support threshold, or
• Use approximation

s(X) support of X
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Approach 3 Using Domain Knowledge

• Approach
• Compute expected support using item taxonomy
• If actual support much lower than expected
  support, then declare it as a negative itemset
• Challenges
• there could be multiple taxonomies (based on
  brand, size, etc)
• limited to nodes that are directly connected to
  the frequent itemsets

Suppose C and G are frequent
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Approach 3 Using Domain Knowledge

• A negative itemset is a set of items whose actual
  support is significantly lower than its expected
  support
• Negative association rule X ? Y
• Rule interest measure
• Approach
• Find frequent itemsets at each level of the
  taxonomy
• Identify candidate negative itemsets based on the
  frequent itemsets found and their item taxonomy
• Count actual support of candidate itemsets and
  retain only the negative itemsets
• Generate negative association rules from negative
  itemsets

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Approach 4 Indirect Association
a
M
b
THEN a and b are expected to occur frequently
together

• a and b are indirectly associated via mediator M
• M identifies the context in which the negative
  association is interesting

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When does Indirect Association become interesting?
For all pairs of items
With Mediator
No Mediator
FM
FN
Frequent
Minimum itempair support
IM
IN
If
Infrequent
IM/FM IN/FN
then Indirect Association is not surprising
mediator thresholds
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Finding Interesting Negative Associations
With Mediator
No Mediator

• IM/FM is small
• IM/IN is small
• ? Indirect Association is interesting

Frequent
FM
FN
Infrequent
IN
IM
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Finding Interesting Negative Association
Indirect Association is interesting when minimum
itempair support threshold is small. But, if
threshold is too low, very few indirect
associations are obtained.
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Grouping Indirect Associations

• Indirect associations can be grouped together
  into more compact structures if they have same
  mediator

Check degree of association
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Mining Indirect Associations
Join step
Prune step
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Application LA-Times
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Application LA-Times
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Application LA-Times
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Application Reuters-21578 news

• Indirect association can identify different
  contexts of a word

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Application Reuters-21578 news
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Application Reuters-21578 news
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Application Retail Data

• Indirect association can identify competing
  (sometimes) complementary items

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Application Retail Data

• Note There is no checkered-flag border wallpaper