# Based on the following data, answer question a, b and c

Based on the following data, answer question a, b and c (6 points)

Customer ID Transaction ID Items bought
1
1
2
2
3
3
4
4
5
5
0001
0024
0012
0031
0015
0022
0029
0040
0033
0038 {a, d, e}
{ a, b, c, e }
{ a, b, d, e }
{ a, c, d, e }
{ b, c, e }
{ b, d, e }
{ c, d}
{ a, b, e }
{ a, d, e }
{ a, b, e }

Compute the support for items{e}, {b, d} and {b, d, e} by treating each transaction ID as a market basket
{e}: support → 8/10 = 80%
{b,d}: support → 2/10 = 20%
{b,d,e}: support → 2/5 = 20%
Use the results in part (a) to compute the confidence for the association rules
{ b, d}→ {e} and {e}→{b, d}. Is confidence a symmetric measure?
{b,d} → {e}: confidence → 2/2 = 100%

● {e} →{b,d}: confidence → 2/8 = 25%

Confidence is not a symmetric measurement.
Repeat part (a) by treating each customer ID as a market basket. Each item should be treated as a binary variable (1 if an item appears in at least one transaction bought by the customer, and 0 otherwise.)
{e}: support → 4/5 = 80%.

● {b,d}: support → 5/5 = 100%

● {b,d,e}: support → 4/5 = 80%
For each of the following measures, determine whether it is monotone, anti-monotone, or non-monotone ( i.e neither monotone nor anti-monotone).
Support, s = ( δ(X))/(∣T∣) is anti-monotone because s(X) ≥ s(Y) whenever X c Y (3 points)

A characteristic rule is the rule of the form {p}→{q1, q2, ……qn }, where the rule antecedent contains only a single item. An itemset of size k can produce up to k characteristic rules. Let ζ be the minimum confidence of all characteristic rules generated from a given itemset:
ζ ({p1, p2, ……pk}) = min [ c({p1 }→ {p2, p3 ……….pk}……
c({pk }→ {p1, p3 ……….pk-1}]
Is ζ monotone, anti-monotone or non-monotone ?

From the following table itemsets, answer the subsequent questions. (6 points)

1
2
3
4
5
6
7
8
9
10 {milk, beer, diapers, }
beer, diapers}