Chapter 27: Problem 5

What is the downward closure property? How does it aid in developing an efficient algorithm for finding association rules, i.e., with regard to finding large itemsets?

Short Answer

Expert verified

The downward closure property, prevalent in data mining, insists that for a set to be 'frequent', its subsets should also be frequent. It aids in effectively pruning search spaces while locating frequent itemsets by eliminating itemsets that have an infrequent subset. This, in turn, allows algorithms for finding association rules to focus on likely large itemsets, reducing computation efforts and optimizing efficiency.

Step by step solution

Define Downward Closure Property

The Downward Closure Property is a fundamental concept in data mining, specifically used in association rule learning. It states that for a set to be considered 'frequent' (or 'large'), all of its subsets must also be frequent. This property is also known as the 'anti-monotone property'.

Explain Working

When it comes to the task of finding frequent itemsets in a large database, the downward closure property can be highly useful. It allows us to systematically prune the search space and disregard any itemset that has an infrequent subset. This is based on the simple principle - if a subset is not frequent, the larger set that contains this subset cannot be frequent. Thus, we do not need to explore larger, potentially less frequent itemsets that contain an infrequent subset.

Discuss Efficiency in Finding Large Itemsets

The downward closure property significantly aids in developing an efficient algorithm for finding large itemsets, primarily because it allows considerable reduction of the search space. It eliminates any need to check larger sets that include an infrequent subset, thereby reducing compute requirements and allowing algorithms to focus on more probable large itemsets. The property directs the search towards truly large itemsets by skipping over large amounts of unlikely candidates.

Connect to Association Rule Learning

In association rule learning, large itemsets are crucial as they form the basis of strong association rules. By being able to identify these large itemsets more efficiently using the downward closure property, the overall process of generating association rules is expedited. More rules can be generated in less time, thereby improving the effectiveness and efficiency of the algorithm.

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What is the downward closure property? How does it aid in developing an efficient algorithm for finding association rules, i.e., with regard to finding large itemsets?

Short Answer

Step by step solution

Define Downward Closure Property

Explain Working

Discuss Efficiency in Finding Large Itemsets

Connect to Association Rule Learning

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