ItemSet Pattern

class paspailleur.bip.ItemSetPattern(value: PatternValueType)

A class representing a set of items as a pattern.

This class allows for the creation and manipulation of patterns that consist of a set of items. It supports operations such as union, intersection, and difference.

References

Agrawal, R., & Srikant, R. (1994). Fast algorithms for mining association rules in large databases.

Attributes

PatternValueType:

The type of the pattern’s value, which is a frozenset.

Properties

value

Return the value of the item set pattern

atomic_patterns

Return the set of all less precise patterns that cannot be obtained by intersection of other patterns.

min_pattern

Return the minimal possible pattern for the item set pattern.

PatternValueType

alias of frozenset

property value: frozenset

Return the value of the item set pattern.

Returns:

value – The value of the itemset pattern, so the set of items itself.

Return type:

PatternValueType

Examples

>>> p = ItemSetPattern({1, 2, 3})
>>> p.value
frozenset({1, 2, 3})

classmethod parse_string_description(value: str) → frozenset

Parse a string description into an item set pattern value.

Parameters:

value (str) – The string description of the item set pattern.

Returns:

parsed – The parsed item set pattern value.

Return type:

PatternValueType

Raises:

ValueError – If the value cannot be parsed into an ItemSetPattern object.

Examples

>>> ItemSetPattern.parse_string_description('{1, 2, 3}')
frozenset({1, 2, 3})

classmethod preprocess_value(value: Collection) → frozenset

Preprocess the value before storing it in the item set pattern.

Parameters:

value (Collection) – The value to preprocess.

Returns:

value – The preprocessed value as a frozenset.

Return type:

frozenset

Examples

>>> ItemSetPattern.preprocess_value([1, 2, 2])
frozenset({1, 2})

atomise(atoms_configuration: Literal['min', 'max'] = 'min') → set[Self]

Split the pattern into atomic patterns, i.e. ItemSets containing just one item.

Parameters:

atoms_configuration (Literal['min', 'max']) – Specifically for ItemSetPattern, the value of atoms_configuration parameter does not affect the output of the function.

Returns:

atomic_patterns – The set of atomic patterns, i.e. the set of unsplittable patterns whose join equals to the pattern.

Return type:

set[Self]

Notes

Speaking in terms of Ordered Set Theory: We say that every pattern can be represented as the join of a subset of atomic patterns, that are join-irreducible elements of the lattice of all patterns.

Considering the set of atomic patterns as a partially ordered set (where the order follows the order on patterns), every pattern can be represented by an _antichain_ of atomic patterns (when atoms_configuration = ‘min’), and by an order ideal of atomic patterns (when atoms_configuration = ‘max’).

property atomic_patterns: set[Self]

Return the set of all less precise patterns that cannot be obtained by intersection of other patterns.

For an ItemSetPattern an atomic pattern is a pattern containing one itme.

Returns:

atoms – A set of atomic patterns, each containing a single item from the item set pattern.

Return type:

set[Self]

Examples

>>> p = ItemSetPattern({1, 2})
>>> p.atomic_patterns
{ItemSetPattern({1}), ItemSetPattern({2})}

classmethod get_min_pattern() → Self

Return the minimal possible pattern, i.e. empty ItemSetPattern

Returns:

The minimal item set pattern, which is an empty frozenset. None if undefined

Return type:

Self

Examples

>>> ItemSetPattern.get_min_pattern()
ItemSetPattern(frozenset())