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fcaR (version 1.5.0)

FormalContext: R6 class for a formal context

Description

This class implements the data structure and methods for formal contexts.

Arguments

Public fields

I

The table of the formal context as a matrix.

attributes

The attributes of the formal context.

objects

The objects of the formal context.

grades_set

The set of degrees (in [0, 1]) the whole set of attributes can take.

expanded_grades_set

The set of degrees (in [0, 1]) each attribute can take.

concepts

The concept lattice associated to the formal context as a ConceptLattice.

implications

A set of implications on the formal context as an ImplicationSet.

description

An optional description of the dataset

Methods

Method new()

Creator for the Formal Context class

Usage

FormalContext$new(I, filename, remove_const = FALSE)

Arguments

I

(numeric matrix) The table of the formal context.

filename

(character) Path of a file to import.

remove_const

(logical) If TRUE, remove constant columns. The default is FALSE.

Details

Columns of I should be named, since they are the names of the attributes of the formal context.

If no I is used, the resulting FormalContext will be empty and not usable unless for loading a previously saved one. In this case, one can provide a filename to import. Only RDS, CSV and CXT files are currently supported.

If the file is not present, the fcarepository.org is looked for coincidences. If so, the corresponding context is loaded.

Returns

An object of the FormalContext class.

Method is_empty()

Check if the FormalContext is empty

Usage

FormalContext$is_empty()

Returns

TRUE if the FormalContext is empty, that is, has not been provided with a matrix, and FALSE otherwise.

Method scale()

Scale the context

Usage

FormalContext$scale(attributes, type, ...)

Arguments

attributes

The attributes to scale

type

Type of scaling.

...

Details

The types of scaling are implemented in a registry, so that scalingRegistry$get_entries() returns all types.

In the dots argument, the user can supply the value for bg (logical), which, if set to TRUE, indicates to compute background knowledge as implications on the scales; if FALSE, no implications will be computed on the scales.

Returns

The scaled formal context

Examples

filename <- system.file("contexts", "aromatic.csv", package = "fcaR")
fc <- FormalContext$new(filename)
fc$scale("nitro", "ordinal", comparison = `>=`, values = 1:3)
fc$scale("OS", "nominal", c("O", "S"))
fc$scale(attributes = "ring", type = "nominal")

Method get_scales()

Scales applied to the formal context

Usage

FormalContext$get_scales(attributes = names(private$scales))

Arguments

attributes

(character) Name of the attributes for which scales (if applied) are returned.

Returns

The scales that have been applied to the specified attributes of the formal context. If no attributes are passed, then all applied scales are returned.

Examples

filename <- system.file("contexts", "aromatic.csv", package = "fcaR")
fc <- FormalContext$new(filename)
fc$scale("nitro", "ordinal", comparison = `>=`, values = 1:3)
fc$scale("OS", "nominal", c("O", "S"))
fc$scale(attributes = "ring", type = "nominal")
fc$get_scales()

Method background_knowledge()

Background knowledge of a scaled formal context

Usage

FormalContext$background_knowledge()

Returns

An ImplicationSet with the implications extracted from the application of scales.

Examples

filename <- system.file("contexts", "aromatic.csv", package = "fcaR")
fc <- FormalContext$new(filename)
fc$scale("nitro", "ordinal", comparison = `>=`, values = 1:3)
fc$scale("OS", "nominal", c("O", "S"))
fc$scale(attributes = "ring", type = "nominal")
fc$background_knowledge()

Method dual()

Get the dual formal context

Usage

FormalContext$dual()

Returns

A FormalContext where objects and attributes have interchanged their roles.

Method intent()

Get the intent of a fuzzy set of objects

Usage

FormalContext$intent(S)

Arguments

S

(Set) The set of objects to compute the intent for.

Returns

A Set with the intent.

Method uparrow()

Get the intent of a fuzzy set of objects

Usage

FormalContext$uparrow(S)

Arguments

S

(Set) The set of objects to compute the intent for.

Returns

A Set with the intent.

Method extent()

Get the extent of a fuzzy set of attributes

Usage

FormalContext$extent(S)

Arguments

S

(Set) The set of attributes to compute the extent for.

Returns

A Set with the intent.

Method downarrow()

Get the extent of a fuzzy set of attributes

Usage

FormalContext$downarrow(S)

Arguments

S

(Set) The set of attributes to compute the extent for.

Returns

A Set with the intent.

Method closure()

Get the closure of a fuzzy set of attributes

Usage

FormalContext$closure(S)

Arguments

S

(Set) The set of attributes to compute the closure for.

Returns

A Set with the closure.

Method obj_concept()

Object Concept

Usage

FormalContext$obj_concept(object)

Arguments

object

(character) Name of the object to compute its associated concept

Returns

The object concept associated to the object given.

Method att_concept()

Attribute Concept

Usage

FormalContext$att_concept(attribute)

Arguments

attribute

(character) Name of the attribute to compute its associated concept

Returns

The attribute concept associated to the attribute given.

Method is_concept()

Is a Concept?

Usage

FormalContext$is_concept(C)

Arguments

C

A Concept object

Returns

TRUE if C is a concept.

Method is_closed()

Testing closure of attribute sets

Usage

FormalContext$is_closed(S)

Arguments

S

A Set of attributes

Returns

TRUE if the set S is closed in this formal context.

Method clarify()

Clarify a formal context

Usage

FormalContext$clarify(copy = FALSE)

Arguments

copy

(logical) If TRUE, a new FormalContext object is created with the clarified context, otherwise the current one is overwritten.

Returns

The clarified FormalContext.

Method reduce()

Reduce a formal context

Usage

FormalContext$reduce(copy = FALSE)

Arguments

copy

(logical) If TRUE, a new FormalContext object is created with the clarified and reduced context, otherwise the current one is overwritten.

Returns

The clarified and reduced FormalContext.

Method standardize()

Build the Standard Context

Usage

FormalContext$standardize()

Details

All concepts must be previously computed.

Returns

The standard context using the join- and meet- irreducible elements.

Method find_concepts()

Use Ganter Algorithm to compute concepts

Usage

FormalContext$find_concepts(method = "InClose", verbose = FALSE)

Arguments

method

(string) The name of a method for the computation of concepts. Available options can be listed with conceptRegistry$get_entries().

verbose

(logical) TRUE will provide a verbose output.

Returns

A list with all the concepts in the formal context.

Method find_implications()

Use modified Ganter algorithm to compute both concepts and implications

Usage

FormalContext$find_implications(save_concepts = TRUE, verbose = FALSE)

Arguments

save_concepts

(logical) TRUE will also compute and save the concept lattice. FALSE is usually faster, since it only computes implications.

verbose

(logical) TRUE will provide a verbose output.

Returns

Nothing, just updates the internal fields concepts and implications.

Method find_causal_rules()

Find causal rules

Usage

FormalContext$find_causal_rules(
  response_var,
  min_support = 0.1,
  confidence_level = 0.95,
  max_length = 3,
  verbose = FALSE
)

Arguments

response_var

(character) The name of the response variable.

min_support

(numeric) Minimum support for the premise attributes.

confidence_level

(numeric) Confidence level for the causality test.

max_length

(integer) Maximum length of the premise.

verbose

(logical) Show verbose output.

Returns

A RuleSet object containing the discovered causal rules and their quality metrics.

Method factorize()

Factorize the formal context using Boolean/Fuzzy Matrix Factorization algorithms.

Usage

FormalContext$factorize(method = "GreConD", ...)

Arguments

method

(character) The algorithm to use. Currently supported: "GreConD", "ASSO".

...

Additional arguments:

  • For GreConD: w (weight, default 1.0), stop_threshold_ratio (error tolerance, default 0.0).

  • For ASSO: threshold (confidence threshold, default 0.7), w_pos (reward), w_neg (penalty).

Returns

A list with two FormalContext objects:

  • object_factor: The context mapping Objects to Factors (Matrix A).

  • factor_attribute: The context mapping Factors to Attributes (Matrix B).

Method to_transactions()

Convert the formal context to object of class transactions from the arules package

Usage

FormalContext$to_transactions()

Returns

A transactions object.

Method save()

Save a FormalContext to RDS or CXT format

Usage

FormalContext$save(filename = tempfile(fileext = ".rds"))

Arguments

filename

(character) Path of the file where to store the FormalContext.

Details

The format is inferred from the extension of the filename.

Returns

Invisibly the current FormalContext.

Method load()

Load a FormalContext from a file

Usage

FormalContext$load(filename)

Arguments

filename

(character) Path of the file to load the FormalContext from.

Details

Currently, only RDS, CSV and CXT files are supported.

Returns

The loaded FormalContext.

Method dim()

Dimensions of the formal context

Usage

FormalContext$dim()

Returns

A vector with (number of objects, number of attributes).

Method to_json()

Export the formal context to JSON

Usage

FormalContext$to_json(file = NULL)

Arguments

file

(character) The path of the file to save the JSON to.

Returns

A JSON string representing the formal context.

Method print()

Prints the formal context

Usage

FormalContext$print()

Returns

Prints information regarding the formal context.

Method to_latex()

Write the context in LaTeX format

Usage

FormalContext$to_latex(table = TRUE, label = "", caption = "")

Arguments

table

(logical) If TRUE, surrounds everything between \begin{table} and \end{table}.

label

(character) The label for the table environment.

caption

(character) The caption of the table.

fraction

(character) If none, no fractions are produced. Otherwise, if it is frac, dfrac or sfrac, decimal numbers are represented as fractions with the corresponding LaTeX typesetting.

Returns

A table environment in LaTeX.

Method incidence()

Incidence matrix of the formal context

Usage

FormalContext$incidence()

Returns

The incidence matrix of the formal context

Examples

fc <- FormalContext$new(planets)
fc$incidence()

Method subcontext()

Generates a new FormalContext restricted to a subset of objects and/or attributes.

Usage

FormalContext$subcontext(objects, attributes)

Arguments

objects

(character or integer vector) The names or indices of the objects to keep. If NULL, keeps all.

attributes

(character or integer vector) The names or indices of the attributes to keep. If NULL, keeps all.

Returns

A new FormalContext object representing the subcontext.

Examples

fc <- FormalContext$new(planets)
fc$subcontext(attributes = c("moon", "no_moon"))

Method [()

Subcontext of the formal context

Usage

FormalContext$[(objects, attributes)

Arguments

objects

(character array) Name of the objects to keep.

attributes

(character array) Names of the attributes to keep.

Details

A warning will be issued if any of the names is not present in the list of objects or attributes of the formal context.

If objects or attributes is empty, then it is assumed to represent the whole set of objects or attributes of the original formal context.

Returns

Another FormalContext that is a subcontext of the original one, with only the objects and attributes selected.

Examples

fc <- FormalContext$new(planets)
fc[, c("moon", "no_moon")]

Method plot()

Plot the formal context table

Usage

FormalContext$plot(to_latex = FALSE, ...)

Arguments

to_latex

(logical) If TRUE, export the plot as a tikzpicture environment that can be included in a LaTeX file.

...

Other parameters to be passed to the tikzDevice that renders the lattice in LaTeX, or for the figure caption. See Details.

Details

Particular parameters that control the size of the tikz output are: width, height (both in inches), and pointsize (in points), that should be set to the font size used in the documentclass header in the LaTeX file where the code is to be inserted.

If a caption is provided, the whole tikz picture will be wrapped by a figure environment and the caption set.

Returns

If to_latex is FALSE, it returns nothing, just plots the graph of the formal context. Otherwise, this function returns the LaTeX code to reproduce the formal context plot.

Method use_logic()

Sets the logic to use

Usage

FormalContext$use_logic(name = available_logics())

Arguments

name

The name of the logic to use. To see the available names, run available_logics().

Method get_logic()

Gets the logic used

Usage

FormalContext$get_logic()

Returns

A string with the name of the logic.

Method use_connection()

Sets the name of the Galois connection to use

Usage

FormalContext$use_connection(connection)

Arguments

connection

The name of the Galois connection. Available connections are "standard" (antitone), "benevolent1" and "benevolent2" (isotone)

Method get_connection()

Gets the name of the Galois connection

Usage

FormalContext$get_connection()

Returns

A string with the name of the Galois connection

Method clone()

The objects of this class are cloneable with this method.

Usage

FormalContext$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

References

Guigues J, Duquenne V (1986). “Familles minimales d'implications informatives résultant d'un tableau de données binaires.” Mathématiques et Sciences humaines, 95, 5-18.

Ganter B, Wille R (1999). Formal concept analysis : mathematical foundations. Springer. ISBN 3540627715.

Belohlavek R (2002). “Algorithms for fuzzy concept lattices.” In Proc. Fourth Int. Conf. on Recent Advances in Soft Computing. Nottingham, United Kingdom, 200-205.

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.

Examples

Run this code
# Build and print the formal context
fc_planets <- FormalContext$new(planets)
print(fc_planets)

# Define a set of attributes
S <- Set$new(attributes = fc_planets$attributes)
S$assign(moon = 1, large = 1)

# Compute the closure of S
Sc <- fc_planets$closure(S)
# Is Sc a closed set?
fc_planets$is_closed(Sc)

# Clarify and reduce the formal context
fc2 <- fc_planets$reduce(TRUE)

# Find implications
fc_planets$find_implications()

# Read a formal context from CSV
filename <- system.file("contexts", "airlines.csv", package = "fcaR")
fc <- FormalContext$new(filename)

# Read a formal context from a CXT file
filename <- system.file("contexts", "lives_in_water.cxt", package = "fcaR")
fc <- FormalContext$new(filename)


## ------------------------------------------------
## Method `FormalContext$scale`
## ------------------------------------------------

filename <- system.file("contexts", "aromatic.csv", package = "fcaR")
fc <- FormalContext$new(filename)
fc$scale("nitro", "ordinal", comparison = `>=`, values = 1:3)
fc$scale("OS", "nominal", c("O", "S"))
fc$scale(attributes = "ring", type = "nominal")

## ------------------------------------------------
## Method `FormalContext$get_scales`
## ------------------------------------------------

filename <- system.file("contexts", "aromatic.csv", package = "fcaR")
fc <- FormalContext$new(filename)
fc$scale("nitro", "ordinal", comparison = `>=`, values = 1:3)
fc$scale("OS", "nominal", c("O", "S"))
fc$scale(attributes = "ring", type = "nominal")
fc$get_scales()

## ------------------------------------------------
## Method `FormalContext$background_knowledge`
## ------------------------------------------------

filename <- system.file("contexts", "aromatic.csv", package = "fcaR")
fc <- FormalContext$new(filename)
fc$scale("nitro", "ordinal", comparison = `>=`, values = 1:3)
fc$scale("OS", "nominal", c("O", "S"))
fc$scale(attributes = "ring", type = "nominal")
fc$background_knowledge()

## ------------------------------------------------
## Method `FormalContext$incidence`
## ------------------------------------------------

fc <- FormalContext$new(planets)
fc$incidence()

## ------------------------------------------------
## Method `FormalContext$subcontext`
## ------------------------------------------------

fc <- FormalContext$new(planets)
fc$subcontext(attributes = c("moon", "no_moon"))

## ------------------------------------------------
## Method `FormalContext$[`
## ------------------------------------------------

fc <- FormalContext$new(planets)
fc[, c("moon", "no_moon")]

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