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Chapter 5 Problems

Use the following table to answer questions 1 and 2.

Need to refer following Videos to answer this calculations:5A) https://s3.us-east-1.amazonaws.com/blackboard.learn.xythos.prod/5a31b16bb2c48/5123411?response-content-disposition=inline%3B%20filename%2 1

1a. Identify a rule that has reasonably high support, but low confidence. Only state the rule; nothing more.

1b. Identify a rule that has low support and high confidence. Only state the rule; nothing more.

1c. Identify a rule that has high support and high confidence. Only state the rule; nothing more.

1d. Identify a rule that has low support and low confidence. Only state the rule; nothing more.

2a. By treating each transaction ID as a market basket, compute the support for each of the following itemsets:

s({e}) =

s({b,d}) =

s({b, d, e}) =

2b. Compute the confidence for the following association rules:

c(b,d  e) =

c(e  b,d) =

2c. By treating each Customer ID as a market basket and treating each item as a binary variable where appearance of an item = 1 in which the customer bought the item (and a 0 otherwise), compute the support for each of the following itemsets:

s({e}) =

s({b,d}) =

s({b, d, e}) =

2d. Use your results in 2c to the confidence for the following association rules:

c(b,d  e) =

c(e  b,d) =

Use the following market basket transactions to answer items in question 3.

3a. What is the maximum number of association rules that can be extracted from this data?

note: be sure to show your calculations

4. The following market basket transactions were used to create the itemset lattice that is next to the market basket. A candidate is discarded if any one of its subsets is found to be infrequent during the candidate pruning step. Support the Apriori algorithm is applied to the data set with minsup = 30%, any itemset occurring in less than 3 transactions is considered to be infrequent.

(a)

Complete the grid below in order to label each node in the lattice with the following letters:

Note: Begin by entering every itemset from the lattice into the table below. You may need to expand the grid in order to accommodate all of your responses.

If the itemset is not considered to be a candidate itemset y the Apriori algorithm. Two reasons for an itemset not to be considered as a candidate itemset: a) it is not generated at all during the candidate generation step, or b) it is generated during the candidate generation step but is subsequently removed during the candidate pruning step because one of its subsets is found to be infrequent.

If the candidate itemset is found to be frequent by the Apriori algorithm.

I: If the candidate itemset is found to be infrequent after support counting.

Itemset	Assigned letter (N, F, or I)

(b)

What is the percentage of frequent itemsets (with respect do all itemsets in the lattice)?

Answer:

(c)

What is the pruning ratio of the Apriori algorithm on this data set? (Pruning ratio is deﬁned as the percentage of itemsets not considered to be a candidate because (1) they are not generated during candidate generation or (2) they are pruned during the candidate pruning step.)

Answer:

Chapter 6 Problems

Use the following table to answer question #1.

1a. Using an Excel spreadsheet, create a binarized version of the data set with the following categories:

Note: the following are also the itemset names in the spreadsheet)

Sky Fair, Sky Stormy, Status Impaired, Status Sober, Violation None, Violation Speeding, Violation Stop, Violation Signal, Restraint = No, Restraint=Yes, Crash Major, Crash Minor

Paste the Excel spreadsheet into this document here.

1b. What is the maximum width of each transaction in the binarized data?

1c. How did you determine the answer for item 1b?

1d. Assuming that support threshold is 30%, how many candidate and frequent itemsets will be generated?

1e. Again using Excel, create a data set that contains only the following asymmetric binary attributes:

(Weather = Bad, Impaired, Traffic violation = Yes, Restraint = No, Crash Severity = Major).

The itemset headings are: Bad, Impaired, Violdation, NoRestraint, and Major

For Traffic violation, only None has a value of 0. The rest of the attribute values are assigned to 1.

Copy and paste the Excel spreadsheet here:

Assuming that support threshold is 30%, how many candidate and frequent itemsets will be generated?

1f. Compare the number of candidate and frequent itemsets generated in 1(d) and 1(e). What is your analysis?

2. Find all the frequent subsequences with support >= 50% given the sequence shown below. Assume there are no timing constraints imposed on the sequence.