Description Methods References Examples

This class implements the structure needed to store implications and the methods associated.

`new()`

Initialize with an optional name

ImplicationSet$new(...)

`...`

See Details.

Creates and initialize a new `ImplicationSet`

object. It can be done in two ways:
`initialize(name, attributes, lhs, rhs)`

or `initialize(rules)`

In the first way, the only mandatory argument is `attributes`

, (character vector) which is a vector of names of the attributes on which we define the implications. Optional arguments are: `name`

(character string), name of the implication set, `lhs`

(a `dgCMatrix`

), initial LHS of the implications stored and the analogous `rhs`

.

The other way is used to initialize the `ImplicationSet`

object from a `rules`

object from package `arules`

.

A new `ImplicationSet`

object.

`get_attributes()`

Get the names of the attributes

ImplicationSet$get_attributes()

A character vector with the names of the attributes used in the implications.

`[()`

Get a subset of the implication set

ImplicationSet$[(idx)

`idx`

(integer or logical vector) Indices of the implications to extract or remove. If logical vector, only

`TRUE`

elements are retained and the rest discarded.

A new `ImplicationSet`

with only the rules given by the `idx`

indices (if all `idx > 0`

and all but `idx`

if all `idx < 0`

.

`to_arules()`

Convert to arules format

ImplicationSet$to_arules(quality = TRUE)

`quality`

(logical) Compute the interest measures for each rule?

A `rules`

object as used by package `arules`

.

`add()`

Add a precomputed implication set

ImplicationSet$add(...)

`...`

An

`ImplicationSet`

object, a`rules`

object, or a pair`lhs`

,`rhs`

of`SparseSet`

objects or`dgCMatrix`

. The implications to add to this formal context.

Nothing, just updates the internal `implications`

field.

`cardinality()`

Cardinality: Number of implications in the set

ImplicationSet$cardinality()

The cardinality of the implication set.

`is_empty()`

Empty set

ImplicationSet$is_empty()

`TRUE`

if the set of implications is empty, `FALSE`

otherwise.

`size()`

Size: number of attributes in each of LHS and RHS

ImplicationSet$size()

A vector with two components: the number of attributes present in each of the LHS and RHS of each implication in the set.

`closure()`

Compute the semantic closure of a fuzzy set with respect to the implication set

ImplicationSet$closure(S, reduce = FALSE, verbose = FALSE)

`S`

(a

`SparseSet`

object) Fuzzy set to compute its closure. Use class`SparseSet`

to build it.`reduce`

(logical) Reduce the implications using simplification logic?

`verbose`

(logical) Show verbose output?

If `reduce == FALSE`

, the output is a fuzzy set corresponding to the closure of `S`

. If `reduce == TRUE`

, a list with two components: `closure`

, with the closure as above, and `implications`

, the reduced set of implications.

`recommend()`

Generate a recommendation for a subset of the attributes

ImplicationSet$recommend(S, attribute_filter)

`S`

(a vector) Vector with the grades of each attribute (a fuzzy set).

`attribute_filter`

(character vector) Names of the attributes to get recommendation for.

A fuzzy set describing the values of the attributes in `attribute_filter`

within the closure of `S`

.

`apply_rules()`

Apply rules to remove redundancies

ImplicationSet$apply_rules( rules = c("composition", "generalization"), batch_size = 25000L, parallelize = FALSE, reorder = FALSE )

`rules`

(character vector) Names of the rules to use. See

`details`

.`batch_size`

(integer) If the number of rules is large, apply the rules by batches of this size.

`parallelize`

(logical) If possible, should we parallelize the computation among different batches?

`reorder`

(logical) Should the rules be randomly reordered previous to the computation?

Currently, the implemented rules are `"generalization"`

, `"simplification"`

, `"reduction"`

and `"composition"`

.

Nothing, just updates the internal matrices for LHS and RHS.

`to_basis()`

Convert Implications to Canonical Basis

ImplicationSet$to_basis()

The canonical basis of implications obtained from the current `ImplicationSet`

`print()`

Print all implications to text

ImplicationSet$print()

A string with all the implications in the set.

`to_latex()`

Export to LaTeX

ImplicationSet$to_latex( print = TRUE, ncols = 1, numbered = TRUE, numbers = seq(self$cardinality()) )

`print`

(logical) Print to output?

`ncols`

(integer) Number of columns for the output.

`numbered`

(logical) If

`TRUE`

(default), implications will be numbered in the output.`numbers`

(vector) If

`numbered`

, use these elements to enumerate the implications. The default is to enumerate 1, 2, ..., but can be changed.

A string in LaTeX format that prints nicely all the implications.

`get_LHS_matrix()`

Get internal LHS matrix

ImplicationSet$get_LHS_matrix()

A sparse matrix representing the LHS of the implications in the set.

`get_RHS_matrix()`

Get internal RHS matrix

ImplicationSet$get_RHS_matrix()

A sparse matrix representing the RHS of the implications in the set.

`filter()`

Filter implications by attributes in LHS and RHS

ImplicationSet$filter(lhs = NULL, rhs = NULL, drop = FALSE)

`lhs`

(character vector) Names of the attributes to filter the LHS by. If

`NULL`

, no filtering is done on the LHS.`rhs`

(character vector) Names of the attributes to filter the RHS by. If

`NULL`

, no filtering is done on the RHS.`drop`

(logical) Remove the rest of attributes in RHS?

An `ImplicationSet`

that is a subset of the current set, only with those rules which has the attributes in `lhs`

and `rhs`

in their LHS and RHS, respectively.

`support()`

Compute support of each implication

ImplicationSet$support()

A vector with the support of each implication

`clone()`

The objects of this class are cloneable with this method.

ImplicationSet$clone(deep = FALSE)

`deep`

Whether to make a deep clone.

Ganter B, Obiedkov S (2016). Conceptual Exploration. Springer. https://doi.org/10.1007/978-3-662-49291-8

Hahsler M, Grun B, Hornik K (2005). “arules - a computational environment for mining association rules and frequent item sets.” *J Stat Softw*, *14*, 1-25.

Belohlavek R, Cordero P, Enciso M, Mora Á, Vychodil V (2016). “Automated prover for attribute dependencies in data with grades.” *International Journal of Approximate Reasoning*, *70*, 51-67.

Mora A, Cordero P, Enciso M, Fortes I, Aguilera G (2012). “Closure via functional dependence simplification.” *International Journal of Computer Mathematics*, *89*(4), 510-526.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# Build a formal context
fc_planets <- FormalContext$new(planets)
# Find its implication basis
fc_planets$find_implications()
# Print implications
fc_planets$implications
# Cardinality and mean size in the ruleset
fc_planets$implications$cardinality()
sizes <- fc_planets$implications$size()
colMeans(sizes)
# Simplify the implication set
fc_planets$implications$apply_rules("simplification")
``` |

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