Question

Show example transaction data where the rule for X → Y: (a) Both support and confidence are high. (b) Support is high and confidence is low. (c) Support is low and confidence is high. (d) Both support and confidence are low.

Answer 1

solution:

given data:

An association rule consists of an antecedent and a consequence. The implication is co-occurrence, not causality. For a given rule, the item set is a list of all items in the antecedent and the consequent.

Bread, Egg (antecedent)->Milk (Consequent)

Support: This gives you an idea of how frequent an item set is in all transaction. Consider item set 1 =bread and item set 2 = shampoo.

There will be more transactions containing bread than shampoo. Bread will have higher support than shampoo.

Mathematically the support is the fraction of the total number of transactions in which the item set occurs.

Support X-> Y=Transaction Contain both X&Y/ number of transactions

Confidence: The likeliness of occurrence of a consequent on the cart considering the cart already has antecedents. "Confidence is the conditional probability of occurrence of consequent given the antecedent."

Confidence X -> Y=Transaction Contain both X&Y/ Transactions containing X

a)

Both support and confidence are high.

X=milk

Y= Diapers

Milk X -> Y Diapers

Support=3/5=60%

Confidence=3/4=75%

Likelihood of person buying milk with diapers is high

b)

Support is high and confidence is low.

X=milk

Y= cola

Milk X ->Y Cola

Support=2/5=40%

Confidence=2/4=50%

Both are beverages one is healthy other is sugary

c)

Support is low and confidence is high.

X=eggs

Y= Diapers

Eggs X -> Y Diapers

Support=1/5=20%

Confidence=1/1=100%

There is no connection between the two activities.

d)

Both support and confidence are low

X=Bread

Y= Eggs

Bread X -> Y Eggs

Support=1/5=20%

Confidence=1/4=25%

Likelihood of person buying bread and eggs is high, both staple foods.

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