Lift ratio as interestingness ■ An example 11100 Y1100|0000 zlo1111114 Rule Support Confidence X=>Y25% 50% Support and Confidence X=>Z37.50%75% ofⅩ=> z dominates oX and Y, positively correlated X and Z, negatively related
11 Lift Ratio As Interestingness X 1 1 1 1 0 0 0 0 Y 1 1 0 0 0 0 0 0 Z 0 1 1 1 1 1 1 1 Rule Support Confidence X=>Y 25% 50% X=>Z 37.50% 75% ◼An Example: Support and Confidence of X=>Z dominates ◼X and Y, positively correlated, ◼X and Z, negatively related
Lift ratio as interestingness It is a measure of dependent or correlated events Apriori=P(Y) The lift of rule X→>Y Contidence=P(YX P(rX P(X∪Y) Xy P(r P(XP(Y) Lift=I means X and Y are independent events Lift< I means X and y are negatively correlated Lift> I means X and y are positively correlated (better than random) 12
12 Lift Ratio As Interestingness ◼ It is a measure of dependent or correlated events ◼ The lift of rule X => Y Lift = 1 means X and Y are independent events Lift < 1 means X and Y are negatively correlated Lift > 1 means X and Y are positively correlated (better than random) ( ) ( | ) , P Y P Y X lift X Y = ( ) ( ) ( ) P X P Y P X Y or Apriori = P(Y) Confidence=P(Y|X)
AR Mining with Lift ratio (1) To understand what lift ratio is. consider the following 500.000 transactions a 20,000 transactions contain diapers (4 percent 30,000 transactions contain beer(6 percent) 10,000 transactions contain both diapers and beer(2 percent) Confidence measures how much a particular item is dependent on another u When people buy diapers, they also buy beer 50% of the time(10000/20000 The confidence for this rule is 50% 13
13 AR Mining with Lift Ratio (1) ◼ To understand what lift ratio is, consider the following: ◼ 500,000 transactions ◼ 20,000 transactions contain diapers (4 percent) ◼ 30,000 transactions contain beer (6 percent) ◼ 10,000 transactions contain both diapers and beer (2 percent) ◼ Confidence measures how much a particular item is dependent on another. ◼ When people buy diapers, they also buy beer 50% of the time (10,000/20,000). ◼ The confidence for this rule is 50%
AR Mining with Lift ratio (2) The inverse rule could be stated as When people buy beer they also buy diapers 1 /3 of the time(Conf=333%=10,000/30,000 In the absence of any knowledge about what else was bought, the following can be computed People buy diapers 4 percent of the time People buy beer 6 percent of the time a 4% and 6% are called the expected confidence(or baseline likelihood, or A Priori Probability) of buying diapers or beer 14
14 ◼ The inverse rule could be stated as: ◼ When people buy beer they also buy diapers 1/3 of the time (Conf=33.33% = 10,000/30,000). ◼ In the absence of any knowledge about what else was bought, the following can be computed: ◼ People buy diapers 4 percent of the time. ◼ People buy beer 6 percent of the time. ◼ 4% and 6% are called the expected confidence (or baseline likelihood, or A Priori Probability) of buying diapers or beer. AR Mining with Lift Ratio (2)
AR Mining with Lift ratio ( 3) Lift measures the difference between the confidence of a rule and the expected confidence Lift is one measure of the strength of an effect If people who bought diapers also bought beer 8% of the time. then the effect is small if expected confidence is 6% If the confidence is 50%. and lift is more than 8 times(when measured as a ratio), then the interactions between diapers and beer is very strong 15
15 ◼ Lift measures the difference between the confidence of a rule and the expected confidence. ◼ Lift is one measure of the strength of an effect. ◼ If people who bought diapers also bought beer 8% of the time, then the effect is small if expected confidence is 6%. ◼ If the confidence is 50%, and lift is more than 8 times (when measured as a ratio), then the interactions between diapers and beer is very strong. AR Mining with Lift Ratio (3)