Data Mining Numerical Problem

Question:

Suppose we have a transaction dataset from a supermarket, and the following information is available:

40% of all transactions involve the purchase of apples.

60% of all transactions involve the purchase of oranges.

30% of the transactions that purchase apples also purchase oranges.

Based on this information, deduce the non-trivial association rules along with their support and

confidence values.

Answer: 

Given Information: 

Support(apples)=0.40

Support(oranges)=0.60

Confidence(apples →oranges)=0.30

Now we have to calculate support(apples, oranges):

The confidence of the rule $\text{apples} \rightarrow \text{oranges}$is given as 0.30.

Confidence(apples →oranges) = Support(apples ∧ oranges) / Support(apples)

0.3 = Support(apples, oranges) / 0.40

Then, Support(apples, oranges) = 0.30×0.40 = 0.12

Non-Trivial Association Rules:​

​Rule 1: apples →oranges

Rule 2: $\text{oranges} \rightarrow \text{apples}$

Calculate Confidence for $\text{oranges} \rightarrow \text{apples}$:

We already know $\text{Support}(\text{apples}\wedge \text{oranges})=0.12\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$

Confidence of (Oranges, apples) defined as: confidence(oranges, apples) = support(apples, oranges) / support(oranges)

Confidence(oranges →apples)=0.12​/ 0.60 =0.20

Summarize the Association Rules with Support and Confidence:​

Rule 1: $\text{apples} \rightarrow \text{oranges}$