Search for association rules

Association rules identify conditions (antecedents) under which a specific feature (consequent) is present very often.

Scheme:: A => C

If condition A is satisfied, then the feature C is present very often.
Example:: university_edu & middle_age & IT_industry => high_income

People in middle age with university education working in IT industry have very likely a high income.

Antecedent A is usually a set of predicates, and consequent C is a single predicate.

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.

Association 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 \(supp(A) / supp(A \cup \{c\})\).

Usage

dig_associations(
  x,
  antecedent = everything(),
  consequent = everything(),
  disjoint = var_names(colnames(x)),
  excluded = NULL,
  min_length = 0L,
  max_length = Inf,
  min_coverage = 0,
  min_support = 0,
  min_confidence = 0,
  contingency_table = FALSE,
  measures = NULL,
  t_norm = "goguen",
  max_results = Inf,
  verbose = FALSE,
  threads = 1,
  error_context = list(arg_x = "x", arg_antecedent = "antecedent", arg_consequent =
    "consequent", arg_disjoint = "disjoint", arg_excluded = "excluded", arg_min_length =
    "min_length", arg_max_length = "max_length", arg_min_coverage = "min_coverage",
    arg_min_support = "min_support", arg_min_confidence = "min_confidence",
    arg_contingency_table = "contingency_table", arg_measures = "measures", arg_t_norm =
    "t_norm", arg_max_results = "max_results", arg_verbose = "verbose", arg_threads =
    "threads", call = current_env())
)

Arguments

x

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.

antecedent

a tidyselect expression (see tidyselect syntax) specifying the columns to use in the antecedent (left) part of the rules

consequent

a tidyselect expression (see tidyselect syntax) specifying the columns to use in the consequent (right) part of the rules

disjoint

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. If x is prepared with partition(), using the var_names() function on x's column names is a convenient way to create the disjoint vector.

excluded

NULL or a list of character vectors, where each character vector contains the names of columns that must not appear together in a single antecedent.

min_length

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.

max_length

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.

min_coverage

the minimum coverage of a rule in the dataset x. (See Description for the definition of coverage.)

min_support

the minimum support of a rule in the dataset x. (See Description for the definition of support.)

min_confidence

the minimum confidence of a rule in the dataset x. (See Description for the definition of confidence.)

contingency_table

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.

measures

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.

t_norm

a t-norm used to compute conjunction of weights. It must be one of "goedel" (minimum t-norm), "goguen" (product t-norm), or "lukas" (Łukasiewicz t-norm).

max_results

the maximum number of generated conditions to execute the callback function on. If the number of found conditions exceeds max_results, the function stops generating new conditions and returns the results. To avoid long computations during the search, it is recommended to set max_results to a reasonable positive value. Setting max_results to Inf will generate all possible conditions.

verbose

a logical value indicating whether to print progress messages.

threads

the number of threads to use for parallel computation.

error_context

a named list providing context for error messages. This is mainly useful when dig_associations() is called from another function and you want error messages to refer to the argument names of that calling function. The list must contain the following elements:

arg_x - name of the argument x
arg_antecedent - name of the argument antecedent
arg_consequent - name of the argument consequent
arg_disjoint - name of the argument disjoint
arg_excluded - name of the argument excluded
arg_min_length - name of the argument min_length
arg_max_length - name of the argument max_length
arg_min_coverage - name of the argument min_coverage
arg_min_support - name of the argument min_support
arg_min_confidence - name of the argument min_confidence
arg_contingency_table - name of the argument contingency_table
arg_measures - name of the argument measures
arg_t_norm - name of the argument t_norm
arg_max_results - name of the argument max_results
arg_verbose - name of the argument verbose
arg_threads - name of the argument threads

Value

An S3 object, which is an instance of associations and nugget classes, and which is a tibble with found patterns and computed quality measures.

Author

Michal Burda

Examples

d <- partition(mtcars, .breaks = 2)
#> Warning: n same as number of different finite values\neach different finite value is a separate class
#> Warning: n same as number of different finite values\neach different finite value is a separate class
dig_associations(d,
                 antecedent = !starts_with("mpg"),
                 consequent = starts_with("mpg"),
                 min_support = 0.3,
                 min_confidence = 0.8,
                 measures = c("lift", "conviction"))
#> # A tibble: 524 × 10
#>    antecedent        consequent support confidence coverage conseq_support count
#>    <chr>             <chr>        <dbl>      <dbl>    <dbl>          <dbl> <dbl>
#>  1 {carb=(-Inf;4.5]… {mpg=(-In…   0.344      0.846    0.406          0.719    11
#>  2 {carb=(-Inf;4.5]… {mpg=(-In…   0.312      0.909    0.344          0.719    10
#>  3 {am=(-Inf;0.5],c… {mpg=(-In…   0.312      0.909    0.344          0.719    10
#>  4 {am=(-Inf;0.5],c… {mpg=(-In…   0.375      0.857    0.438          0.719    12
#>  5 {carb=(-Inf;4.5]… {mpg=(-In…   0.5        0.889    0.562          0.719    16
#>  6 {carb=(-Inf;4.5]… {mpg=(-In…   0.375      1        0.375          0.719    12
#>  7 {am=(-Inf;0.5],c… {mpg=(-In…   0.375      1        0.375          0.719    12
#>  8 {am=(-Inf;0.5],c… {mpg=(-In…   0.375      1        0.375          0.719    12
#>  9 {am=(-Inf;0.5],c… {mpg=(-In…   0.375      1        0.375          0.719    12
#> 10 {am=(-Inf;0.5],c… {mpg=(-In…   0.375      1        0.375          0.719    12
#> # ℹ 514 more rows
#> # ℹ 3 more variables: antecedent_length <int>, lift <dbl>, conviction <dbl>

Usage

Arguments

Value

See also

Author

Examples