1. Interestingness

2. Interestingness Measures - Lift
Measure of dependent/correlated events: lift
Lift(B, C) = c(B->C)/s(C) = s(B u C)/(s(B) x s(C))
Lift(B, C) may tell how B and C are correlated
Lift(B, C) = 1 => B and C are independent
> 1: positively correlated
< 1: negatively correlated
Lift is more telling than support (s) & confidence (c)

3. Lift Example B ^B Tot Row C 400 350 750 ^C 200 50 250 Total Column 600
1000

4. Lift Solution Lift(B, C) = (400/1000)/((600/1000)*(750/1000)) = 0.89
Tot Row C
400
350
750 ^C
200 50
250
Total Column
600
1000
Lift(B, C) = (400/1000)/((600/1000)*(750/1000)) = 0.89
Lift(B, ^C) = (200/1000)/((600/1000)*(250/1000)) = 1.33
Thus B & C are negatively correlated since Lift(B,C) < 1
B and ^C are positively correlated since Lift(B, ^C) > 1

5. Lift Calculations s(B u C) =400/1000 = 2/5 = .4
s(C) = 750/1000 = ¾ = .75
Lift(B, C) = .4/(.6*.75) = .4/.45 = .89
s(B u ^C) = .2
s(B) = .6
s(^C) = .25
Lift(B, ^C) = .2/.15 = 1.33
Lift(^B, C) = ?
Lift(^B, ^C) = ?

6. Interestingness Measures - c2
Another measure to test correlated events: c2
c2 = Σ (Observed – Expected)2 / Expected
General rules
c2 = 0 => independent
c2 > 0 => correlated, either positively or negatively, so it needs additional tests.
C2 also tells better than support (s) and confidence (c)

7. c2 Example B ^B Tot Row C 400 (450) 350 (300) 750 ^C 200 (150)
50 (100)
250
Total Column
600
400
1000

8. c2 Solution B ^B
Tot Row C
400 (450)
350 (300)
750 ^C
200 (150)
50 (100)
250
Total Column
600
400
1000
Now c2 = ( ) 2/450 + ( ) 2/300 + ( ) 2/ (50-100) 2/100 = 55.55
c2 Shows B & C are correlated because the answer > 0
As expected value is 450 but 400 is observed we can say that B & C are negatively correlated.

9. Are Lift and c2 Always Good?
Null transactions -> transactions that contain neither B nor C
Let’s examine another dataset D
BC (100) is much rarer than B^C(1000) and ^BC (1000), but there are many ^B^C (100000)
So unlikely that B&C will happen together!
But, Lift(B,C) = 8.44 >> 1 (strong positive correlation)
c2 i= 670 : Observed (BC) >> expected value (11.85)
Too many null transactions may “spoil the soup”!

10. c2 & Lift With Null ExampleB ^B
Tot Row C
100 (11.85)
1000
1100 ^C
200 (988.15)
100000
101000
Total Column
102100

11. Other Interestingness Algorithms
Null invariance – value does not change with the number of null transactions.
Interestingness null invariance measures:
AllConf(A,B)
Jaccard(A,B)
Cosine(A,B)
Kulczynski(A,B)
MaxConf(A,B)
Not all null-invariant measures are created equal

12. Imbalance Ratio with Kulczynski
Imbalance Ratio: measure the imbalance of two itemsets A&B in rule implications

13. Kulczynski (P(B/C) + P(C/B))/2 < epsilon where epsilon is 0.01
Where A = milk, b = coffee
1 billion transaction = 1,000,000,000
A = 1 million time = 1,000,000
B = 10 thousand times = 10000
A + B = one hundred = 100
S(A) = 10^6 / 10^9 = 10^-3 = 1/1000
S(B) = 10^4/ 10^9 = 10^-5 = 1/100000
S(A u B) = 10^2 / 10^9 = 10^-7 = 1/
S(A) * S(B) = 10^-3*10^-5 = 10^-8

14. Kulczynski P(B|A) = P(AUB) / P(A) = 10^2/10^6 = 10^-4
P(A|B) = P(AUB) / P(B) = 10^2/ 10^4 = 10^-2
(P(B|A) + P(A|B))/2 = (10^ ^-2)/2 = < 0.01
Therefore this is a negative pattern