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, }

{ bread, butter, milk }

{milk, diapers, cookies}

{ bread, butter, cookies }

{beer, cookies , diapers }

{milk, diapers, bread, butter}

{ bread, butter, diapers, }

beer, diapers}

{milk, diapers, bread, butter}

{beer, cookies }

What is the maximum number of association rules that can be extracted from this data (including rules that have zero support)?

What is the maximum size of frequent itemsets that can be extracted (assuming

Min-sup > o)?

Find an itemset (of size 2 or larger) that has the larger support.

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