Question

1. Consider the data set of market basket transactions shown in following table:

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

1. Compute the support(%) for itemsets {e}, {b, d}, and {b, d, e} by treating each transaction ID as a market basket.

2. Use the results in part (a) to compute the confidence for the association rules {b,d} −→ {e} and {e} −→ {b,d}.

3. Is confidence a symmetric measure or an asymmetric measure?
4. 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.)
5. Use the results in part (d) to compute the confidence for the association rules {b, d} −→ {e} and {e} −→ {b, d}.

Answer 1

1. Compute the support(%) for itemsets {e}, {b, d}, and {b, d, e} by treating each transaction ID as a market basket.

ANSWER: Support can be found as the percentage of occurrence in the given table.

Itemset	Transaction ID	Support
{e}	0001, 0012, 0031, 0040, 0033, 0038	6/10 = .6 = 60%
{b, d}	0012, 0015, 0040, 0033	4/10 = .4 = 40%
{b, d, e}	0012, 0040, 0033	3/10 = .3 = 30%

2. Use the results in part (a) to compute the confidence for the association rules {b,d} −→ {e} and {e} −→ {b,d}

ANSWER: Confidence can be calculated as:

Confidence {b,d} −→ {e} = {b,d, e} count / {b,d} count

= 3 / 4 = .75 = 75%

Confidence {e} −→ {b,d} = {e, b,d} count / {e} count

= 3/6 = .5 = 50%

3. Is confidence a symmetric measure or an asymmetric measure?

ANSWER: Based on the result above, confidence is NOT a symmetric measure, because in part B the confidence is different.

4. 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.)

ANSWER: Draw the table according to as per below tab;e and recompute support

Customer ID	a	b	c	d	e	f
1	1	1	1	1	1	1
2	1	1	1	1	1	1
3	1	1	0	1	0	1
4	1	1	1	1	1	0
5	0	1	1	1	1	1

Itemset	Transaction ID	Support
{e}	1, 2, 4, 5	4/5 = .8 = 80%
{b, d}	1, 2, 3, 4, 5	5/5 = 1 = 100%
{b, d, e}	1, 2, 4, 5	4/5 = .8 = 80%

5. Use the results in part (d) to compute the confidence for the association rules {b, d} −→ {e} and {e} −→ {b, d}.

ANSWER: Confidence can be calculated as:

Confidence {b,d} −→ {e} = {b,d, e} count / {b,d} count

= 4 / 5 = .8 =   80%

Confidence {e} −→ {b,d} = {e, b,d} count / {e} count

= 4/4 = 1 = 100%