# Frequent Itemset

A frequent itemset is a dataset subset with an itemset frequency that is greater than some given proportion threshold.

**Context:**- It can be described intensionally by a frequent itemset pattern.
- It can be found by a Frequent Itemset Finding Task.
- It can range from being a Frequent Closed Itemset to being a Frequent Open Itemset.
- It can range from being a Maximal Itemset to being a Minimal Itemset.
- It can range from being a 1 Frequent Item to being a k Frequent Item.
- …

**Example(s):**- a Frequent Word Set,
- …

**Counter-Example(s):****See:**Frequent Pattern, Frequent Pattern Recognition Task, Association Rule, Constraint-Based Mining, Frequent Pattern, Pattern Recognition System, Knowledge Discovery System.

## References

### 2017

- (Toivonen, 2017) ⇒ Hannu Toivonen. (2017). "Frequent Itemset". In: (Sammut & Webb, 2017). DOI: 10.1007/978-1-4899-7687-1_317
- QUOTE: Frequent itemsets (Agrawal et al. 1993, 1996) are a form of frequent pattern. Given examples that are sets of items and a minimum frequency, any set of items that occurs at least in the minimum number of examples is a frequent itemset.
For instance, customers of an on-line bookstore could be considered examples, each represented by the set of books he or she has purchased. A set of books, such as

`{“Machine Learning,” “The Elements of Statistical Learning,” “Pattern Classification,”}`

is a frequent itemset if it has been bought by sufficiently many customers. Given a frequency threshold, perhaps only 0.1 or 0.01 % for an on-line store, all sets of books that have been bought by at least that many customers are called frequent. Discovery of all frequent itemsets is a typical data mining task. The original use has been as part of association rule discovery. Apriori is a classical algorithm for finding frequent itemsets.

- QUOTE: Frequent itemsets (Agrawal et al. 1993, 1996) are a form of frequent pattern. Given examples that are sets of items and a minimum frequency, any set of items that occurs at least in the minimum number of examples is a frequent itemset.

### 2008

- (Wang, 2008) ⇒ John Wang. (2008). “Encyclopedia of Data Warehousing and Mining, 2nd edition." Information Science Reference. ISBN 1605660108
- QUOTE: A frequent itemset is a set of words that occur together in some minimum fraction of documents in a cluster. therefore, a frequent itemset describes something common to many documents in a cluster. They use frequent itemsets to construct clusters and to organize cluster into a topic hierarchy. Yiu & Mamoulis (2003) uses project clustering algorithms to find cluster in hidden subspaces.

### 2004

- (Sivanandam et al., 2004) ⇒ S. N. Sivanandam, D. Sumathi, T. Hamsapriya, and K. Babu. (2004). “Parallel Buddy Prima – A Hybrid Parallel Frequent itemset mining algorithm for very large databases." Retrieved from http://www.acadjournal.com.
- QUOTE: The definition of a frequent pattern relies on the following considerations. A set of items is referred to as an itemset (pattern). An itemset that contains [math]\displaystyle{ k }[/math] items is a k-itemset. The set {X, Y} is a 2- itemset. The occurrence frequency of an itemset is the number of transactions that contain the itemset. This is also known as the frequency or the support count of an itemset. An itemset satisfies minimum support if the occurrence frequency of the itemset is greater than or equal to the minimal support threshold value defined by the user. The number of transactions required for the itemset to satisfy minimum support is therefore referred to as the minimum support count. If an itemset satisfies minimum support, then it is a frequent itemset (frequent pattern).
A frequent itemset is called closed if it does not have any superset with the same support. A frequent itemset is said to be maximal if it has no supersets that are frequent. The collection of maximal frequent itemsets is a subset of the collection of closed frequent itemsets, which is a subset of the collection of all frequent itemsets. Maximal frequent itemsets are necessary for generating association rules.

- QUOTE: The definition of a frequent pattern relies on the following considerations. A set of items is referred to as an itemset (pattern). An itemset that contains [math]\displaystyle{ k }[/math] items is a k-itemset. The set {X, Y} is a 2- itemset. The occurrence frequency of an itemset is the number of transactions that contain the itemset. This is also known as the frequency or the support count of an itemset. An itemset satisfies minimum support if the occurrence frequency of the itemset is greater than or equal to the minimal support threshold value defined by the user. The number of transactions required for the itemset to satisfy minimum support is therefore referred to as the minimum support count. If an itemset satisfies minimum support, then it is a frequent itemset (frequent pattern).