Introduction to the Apriori Algorithm Answers 1. What defines the frequent 2-itemsets based on the given transaction dataset? A. {C, E} (3 times) B. {A, C} (2 times) C. {A, B} (3 times) D. {B, E} (2 times) Answer: {A, B} (3 times) (C) The frequent 2-itemsets include {A, B} which appears 3 times in the transactions. 2. Which statement best describes the efficiency considerations of the Apriori algorithm? A. Reduced search space increases computational requirements. B. It can be computationally expensive due to repeated database scanning. C. The algorithm is more efficient with larger datasets. D. Repeated scans of the data always improve efficiency. Answer: It can be computationally expensive due to repeated database scanning. (B) Efforts to reduce the search space can lead to increased computation due to the need for repeated database scans. 3. What is one variant of the Apriori algorithm mentioned in the content? A. AprioriEnhanced B. AprioriFast C. AprioriTID D. AprioriPlus Answer: AprioriTID (C) AprioriTID is a variant that utilizes transaction IDs to optimize candidate generation and support counting. 4. In the context of frequent itemsets, what is the minimum support threshold set in the example? A. 4 B. 2 C. 1 D. 3 Answer: 2 (B) The minimum support threshold is set at 2, which determines the frequency of itemsets. 5. What is a notable trade-off associated with extensions of the Apriori algorithm? A. Improvement in space requirements without affecting complexity. B. Trade-offs between efficiency gain, computational complexity, and space considerations. C. Increased computational complexity for lower efficiency. D. Higher efficiency at the cost of additional database scans. Answer: Trade-offs between efficiency gain, computational complexity, and space considerations. (B) Extensions of the algorithm often involve trade-offs between efficiency, complexity, and space. 6. What is the primary purpose of the Apriori algorithm? A. To discover frequent itemsets in a dataset B. To predict future trends based on historical data C. To find the most significant outlier in the data D. To classify data into different categories Answer: To discover frequent itemsets in a dataset (A) The Apriori algorithm is specifically used for discovering frequent itemsets, particularly in market basket analysis. 7. Which statement correctly describes the Apriori property? A. If an itemset is infrequent, then at least one of its subsets is also infrequent. B. If an itemset is frequent, then all of its subsets must also be frequent. C. An itemset can only be considered frequent if it has no subsets. D. If a frequent itemset exists, then one of its subsets must be infrequent. Answer: If an itemset is frequent, then all of its subsets must also be frequent. (B) The Apriori property states that if an itemset is frequent, then all of its subsets must also be frequent. 8. What is the first step in the Apriori algorithm? A. Discard infrequent itemsets B. Scan the database for candidate k-itemsets C. Check the frequency of all itemsets D. Generate candidate 1-itemsets Answer: Generate candidate 1-itemsets (D) The first step of the Apriori algorithm is to generate candidate 1-itemsets from the transaction database. 9. During the iterative steps of the Apriori algorithm, candidate kitemsets are generated from which of the following? A. Frequent (k-1)-itemsets B. Frequent k-itemsets only C. All previous candidate itemsets D. Infrequent itemsets Answer: Frequent (k-1)-itemsets (A) Candidate k-itemsets are generated from frequent (k-1)-itemsets in the iterative process of the Apriori algorithm. 10. Which of the following is a condition for merging two (k-1)itemsets to form a candidate k-itemset? A. At least one item must be common between both sets B. The total number of items in both itemsets must be even C. Both itemsets must have unique items D. Their first k-2 items must be identical Answer: Their first k-2 items must be identical (D) Two (k-1)-itemsets can only be merged to form a candidate k-itemset if their first (k-2) items are identical. 11. What is the role of the minimum support threshold in the Apriori algorithm? A. It determines the size of the transaction database. B. It specifies how many items can be in a candidate set. C. It defines the minimum frequency an itemset must have to be considered frequent. D. It sets a maximum limit on the number of transactions processed. Answer: It defines the minimum frequency an itemset must have to be considered frequent. (C) The minimum support threshold is used to determine the frequency that an itemset must achieve to be considered frequent. 12. How does the pruning step in the Apriori algorithm enhance computational efficiency? A. By limiting the number of transactions being analyzed B. By excluding infrequent itemsets that cannot be frequent C. By scanning the database multiple times D. By increasing the size of the candidate itemsets Answer: By excluding infrequent itemsets that cannot be frequent (B) Pruning involves removing itemsets with support below the threshold, helping to reduce the computational cost in finding frequent itemsets. 13. What is the output of the Apriori algorithm? A. Candidate itemsets that could be frequent B. All possible itemsets from the transaction database C. The number of transactions analyzed D. Frequent itemsets that meet the minimum support Answer: Frequent itemsets that meet the minimum support (D) The output of the Apriori algorithm is the frequent itemsets that meet or exceed the defined minimum support threshold.