tiditemset 1 2367 2134811 vegetables grain fruit diary )15 14 33911 4 1567 5 13
ID: 3723485 • Letter: T
Question
tiditemset 1 2367 2134811 vegetables grain fruit diary )15 14 33911 4 1567 5 13 8 10 11 63579 11 bread 12 rce milk )13 cheese 746 8 10 11 8135 8 11 Table 8.5: Dataset for Q6 wheat white rye whole 2% skim 10 Figure 8.10: Item Taxonomy for Q6 Q6. Consider Figure 8.10. It shows a simple taxonomy on some food items. Each leaf is a simple item and an internal node represents a higher-level category or item. Each item (single or high-level) has a unique integer label noted under it. Consider the database composed of the simple items shown in Table 8.5 Answer the following questions (a) What is the size of the itemset search space if one restricts oneself to only itemsets composed of simple items? (b) Let X = {ri, T2, , x be a frequent itemset. Let us replace some xi E X with its parent in the taxonomy (provided it exists), to obtain X', then the support of the new itemset X is i. more than support of X ii. less than support of X ii. not equal to support of X iv. more than or equal to support of X v. less than or equal to support of XExplanation / Answer
(a) The itemset search space will still be the entire item space, since when we consider only the simple items, we still have to go through the higher-level items. So the itemset search space occupies all the items. Hence its size for this Item Taxonomy would be 15.
b) Answer:
(iv) more than or equal to support of X
Explaination:
Support of an itemset if the frequency at which it occurs in one iteration or scan. In the frequent itemset X if an xi is replaced by it's parent, then the frequency of that xi appearing will increase, as reaching the leaf node is rearer than reaching a higher-level node. So if xi is such that you need to pass through it's parent xip then the frequency of xi occuring is equal to the frequency of xip occuring if xi is xip 's only child node, since it would have to scan xip to reach xi. But if xip has more nodes than xi then we will scan xip while visiting those other child nodes as well. Hence the frequency of xip (parent of xi ) will increase and inturn the frequency of the entire itemset X' will increase. So, we can say that on replacing xi with it's parent to obtain X', then the support of X' would be more than or equal to the support of X.
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