Implicative rule is a rule of the form \(A \Rightarrow c\), where \(A\) (antecedent) is a set of predicates and \(c\) (consequent) is a predicate.
dig_implications(
x,
antecedent = everything(),
consequent = everything(),
disjoint = NULL,
min_length = 0L,
max_length = Inf,
min_coverage = 0,
min_support = 0,
min_confidence = 0,
contingency_table = FALSE,
measures = NULL,
t_norm = "goguen",
threads = 1,
...
)A tibble with found rules and computed quality measures.
a matrix or data frame with data to search in. The matrix must be
numeric (double) or logical. If x is a data frame then each column
must be either numeric (double) or logical.
a tidyselect expression (see tidyselect syntax) specifying the columns to use in the antecedent (left) part of the rules
a tidyselect expression (see tidyselect syntax) specifying the columns to use in the consequent (right) part of the rules
an atomic vector of size equal to the number of columns of x
that specifies the groups of predicates: if some elements of the disjoint
vector are equal, then the corresponding columns of x will NOT be
present together in a single condition.
the minimum length, i.e., the minimum number of predicates in the antecedent, of a rule to be generated. Value must be greater or equal to 0. If 0, rules with empty antecedent are generated in the first place.
The maximum length, i.e., the maximum number of predicates in the antecedent, of a rule to be generated. If equal to Inf, the maximum length is limited only by the number of available predicates.
the minimum coverage of a rule in the dataset x.
(See Description for the definition of coverage.)
the minimum support of a rule in the dataset x.
(See Description for the definition of support.)
the minimum confidence of a rule in the dataset x.
(See Description for the definition of confidence.)
a logical value indicating whether to provide a contingency
table for each rule. If TRUE, the columns pp, pn, np, and nn are
added to the output table. These columns contain the number of rows satisfying
the antecedent and the consequent, the antecedent but not the consequent,
the consequent but not the antecedent, and neither the antecedent nor the
consequent, respectively.
a character vector specifying the additional quality measures to compute.
If NULL, no additional measures are computed. Possible values are "lift",
"conviction", "added_value".
See https://mhahsler.github.io/arules/docs/measures
for a description of the measures.
a t-norm used to compute conjunction of weights. It must be one of
"goedel" (minimum t-norm), "goguen" (product t-norm), or "lukas"
(Lukasiewicz t-norm).
the number of threads to use for parallel computation.
Further arguments, currently unused.
Michal Burda
For the following explanations we need a mathematical function \(supp(I)\), which
is defined for a set \(I\) of predicates as a relative frequency of rows satisfying
all predicates from \(I\). For logical data, \(supp(I)\) equals to the relative
frequency of rows, for which all predicates \(i_1, i_2, \ldots, i_n\) from \(I\) are TRUE.
For numerical (double) input, \(supp(I)\) is computed as the mean (over all rows)
of truth degrees of the formula i_1 AND i_2 AND ... AND i_n, where
AND is a triangular norm selected by the t_norm argument.
Implicative rules are characterized with the following quality measures.
Length of a rule is the number of elements in the antecedent.
Coverage of a rule is equal to \(supp(A)\).
Consequent support of a rule is equal to \(supp(\{c\})\).
Support of a rule is equal to \(supp(A \cup \{c\})\).
Confidence of a rule is the fraction \(supp(A) / supp(A \cup \{c\})\).
dig()