Answer the following questions: (10 point each)

- Consider the data set shown in Table 5.1.

**Table 5.1. **Example of market basket transactions.

Customer ID | Transaction ID | Items Bought |

1 | 0001 | {a, d, e} |

2 | 0024 | {a, b, c, e} |

2 | 0012 | {a, b, d, e} |

2 | 0031 | {a, c, d, e} |

3 | 0015 | {b, c, e} |

3 | 0022 | {b, d, e} |

3 | 0029 | {c, d} |

4 | 0040 | {a, b, c} |

5 | 0033 | {a, d, e} |

- Compute the support for item sets
*{e}*,*{b, d}*, and*{b, d, e}*by treating each transaction ID as a market basket.

S({c}) =

S({e, d}) =

S({a, b, d}) =

S({c, d}) =

- Use the results in part (a) to compute the confidence for the association

rules {b, d} à {e} and {e} à {b, d}. Is confidence a symmetric measure?

c(bd à e) =

c(e à bd) =

- Consider the market basket transactions shown in Table 5.2.

**Table 5.2. **Market basket transactions

Transaction ID | Items Bought |

1 | {Milk, Beer, Diapers} |

2 | {Bread, Butter, Milk} |

3 | {Milk, Diapers, Cookies} |

4 | {Bread, Butter, Cookies} |

5 | {Beer, Cookies, Diapers} |

6 | {Milk, Diapers, Bread, Butter, Cheese} |

7 | {Bread, Butter, Diapers} |

8 | {Beer, Diapers} |

9 | {Milk, Diapers, Bread, Butter} |

10 | {Beer, Cookies} |

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

**Answer:**

- What is the maximum size of frequent item sets that can be extracted (assuming
*minusup >*0)?

**Answer:**

- Write an expression for the maximum number of size-3 itemsets that can be derived from this data set.

**Answer:**

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

**Answer:**

- Find a pair of items,
*a*and*b*, such that the rules*{a} → {b}*and*{b} → {a}*have the same confidence.

**Answer: **

The Apriori algorithm uses a generate-and-count strategy for deriving frequent itemsets. Candidate itemsets of size k+1 are created by joining a pair of frequent itemsets of size k (this is known as the candidate generation step). A candidate is discarded if any one of its subsets is found to be infrequent during the candidate pruning step. Suppose the Apriori algorithm is applied to the data set shown in Table 5.3 with minsup = 30%, i.e., any itemset occurring in less than 3 transactions is considered to be infrequent.

**Table 5.3. **Example of market basket transactions.

Transaction ID | Items Bought |

1 | {a, b, c} |

2 | {b, c, d} |

3 | {a, b, d} |

4 | {a, c, d} |

5 | {b, c} |

6 | {c, d} |

7 | {c} |

8 | {a, b, c} |

9 | {a, d} |

10 | {b, d} |

(a) Draw an itemset lattice representing the data set given in Table 5.3.

Label each node in the lattice with the following letter(s):

- N: If the itemset is not considered to be a candidate itemset by the Apriori algorithm. There are two reasons for an itemset not to be considered as a candidate itemset: (1) it is not generated at all during the candidate generation step, or (2) 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.
- F: 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.

**Answer:**

(b) What is the percentage of frequent itemsets (with respect to 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:**

(d) What is the false alarm rate (i.e, percentage of candidate itemsets that are found to be infrequent after performing support counting)?

**Answer:**

Get **Argumentative Essay Writing help** now

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.