itemsetsthose

Itemsetsthose is a theoretical construct used in the field of pattern mining to describe a class of selection operators applied to collections of itemsets. The term combines itemsets with a demonstrative element to emphasize the act of choosing those itemsets that meet a specified condition. While not a universally standardized term, it appears in some theoretical discussions as a convenient way to describe intersection- or predicate-based filtering of itemsets.

Definition and notation: Let S be a set of itemsets drawn from a universe of items. Let P be a predicate that can be evaluated on an itemset s ∈ S. The operator itemsetsthose(S, P) yields the subset { s ∈ S | P(s) is true }. In a common specialization, where P asks for a nonempty intersection with a reference set T, the operator becomes itemsetsthose(S, T) = { s ∈ S | s ∩ T ≠ ∅ }.

Example: Consider S = { {bread, milk}, {bread}, {milk, cheese}, {butter} } and T = {milk, butter}. Then itemsetsthose(S, T) = { {bread, milk}, {milk, cheese}, {butter} }.

Applications: itemsetsthose can be used to filter results in data mining workflows, such as extracting itemsets that involve a particular category (for example dairy products) or preparing input for downstream tasks like association rule mining, clustering, or visualization.

Relation to related concepts: The operator is akin to a selection or filter operation in relational algebra and is related to intersection-based filtering in frequent itemset mining. It is independent of how the initial itemsets were produced and can be applied to any suitable collection.

See also: frequent itemset, closed itemset, association rule, pattern mining.

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