R6 class for a concept lattice

This class implements the data structure and methods for concept lattices.

Super class

fcaR::ConceptSet -> ConceptLattice

Methods

Public methods

• ConceptLattice$new()

• ConceptLattice$plot()

• ConceptLattice$sublattice()

• ConceptLattice$top()

• ConceptLattice$bottom()

• ConceptLattice$join_irreducibles()

• ConceptLattice$meet_irreducibles()

• ConceptLattice$decompose()

• ConceptLattice$supremum()

• ConceptLattice$infimum()

• ConceptLattice$subconcepts()

• ConceptLattice$superconcepts()

• ConceptLattice$lower_neighbours()

• ConceptLattice$upper_neighbours()

• ConceptLattice$stability()

• ConceptLattice$separation()

• ConceptLattice$density()

• ConceptLattice$check_properties()

• ConceptLattice$is_distributive()

• ConceptLattice$is_modular()

• ConceptLattice$clone()

Inherited methods

• fcaR::ConceptSet$[()
• fcaR::ConceptSet$extents()
• fcaR::ConceptSet$intents()
• fcaR::ConceptSet$is_empty()
• fcaR::ConceptSet$print()
• fcaR::ConceptSet$size()
• fcaR::ConceptSet$sub()
• fcaR::ConceptSet$support()
• fcaR::ConceptSet$to_latex()
• fcaR::ConceptSet$to_list()

---

Method new()

Create a new ConceptLattice object.

Usage

ConceptLattice$new(extents, intents, objects, attributes, I = NULL)

Arguments

extents

(dgCMatrix) The extents of all concepts

intents

(dgCMatrix) The intents of all concepts

objects

(character vector) Names of the objects in the formal context

attributes

(character vector) Names of the attributes in the formal context

I

(dgCMatrix) The matrix of the formal context

Returns

A new ConceptLattice object.

---

Method plot()

Plot the concept lattice

Usage

ConceptLattice$plot(
  object_names = TRUE,
  to_latex = FALSE,
  method = c("sugiyama", "force"),
  mode = NULL,
  ...
)

Arguments

object_names

(logical) Deprecated. Use mode instead. If TRUE (default), implies mode = "reduced" or similar depending on heuristics. Kept for backward compatibility.

to_latex

(logical) If TRUE, exports the plot as TikZ code (LaTeX) instead of drawing it. Returns an object of class tikz_code that prints the LaTeX code to console.

method

(character) The layout algorithm to use. Options are:

• "sugiyama" (default): A hierarchical layout that minimizes edge crossings and centers nodes (similar to ConExp or hasseDiagram).

• "force": A force-directed (spring) layout, useful for large or non-hierarchical lattices.

mode

(character) The labeling mode for the nodes. If NULL (default), a heuristic based on lattice size is used. Options are:

• "reduced": Standard FCA labeling. Nodes are labeled with an attribute (or object) only if they are the supreme (or infimum) of that attribute (or object).

• "full": Each node shows its complete extent and intent.

• "attributes": Nodes show only their intent (attributes).

• "empty": Nodes are drawn as points without labels. Recommended for very large lattices (>50 concepts).

...

Other parameters passed to the internal plotting function (e.g., graphical parameters for ggraph).

Returns

If to_latex is FALSE, it returns (invisibly) the ggplot2 object representing the graph. If to_latex is TRUE, it returns a tikz_code object containing the LaTeX code.

---

Method sublattice()

Sublattice

Usage

ConceptLattice$sublattice(...)

Arguments

...

See Details.

Details

As argument, one can provide both integer indices or Concepts, separated by commas. The corresponding concepts are used to generate a sublattice.

Returns

The generated sublattice as a new ConceptLattice object.

---

Method top()

Top of a Lattice

Usage

ConceptLattice$top()

Returns

The top of the Concept Lattice

Examples

fc <- FormalContext$new(planets)
fc$find_concepts()
fc$concepts$top()

---

Method bottom()

Bottom of a Lattice

Usage

ConceptLattice$bottom()

Returns

The bottom of the Concept Lattice

Examples

fc <- FormalContext$new(planets)
fc$find_concepts()
fc$concepts$bottom()

---

Method join_irreducibles()

Join-irreducible Elements

Usage

ConceptLattice$join_irreducibles()

Returns

The join-irreducible elements in the concept lattice.

---

Method meet_irreducibles()

Meet-irreducible Elements

Usage

ConceptLattice$meet_irreducibles()

Returns

The meet-irreducible elements in the concept lattice.

---

Method decompose()

Decompose a concept as the supremum of meet-irreducible concepts

Usage

ConceptLattice$decompose(C)

Arguments

C

A list of Concepts

Returns

A list, each field is the set of meet-irreducible elements whose supremum is the corresponding element in C.

---

Method supremum()

Supremum of Concepts

Usage

ConceptLattice$supremum(...)

Arguments

...

See Details.

Details

As argument, one can provide both integer indices or Concepts, separated by commas. The corresponding concepts are used to compute their supremum in the lattice.

Returns

The supremum of the list of concepts.

---

Method infimum()

Infimum of Concepts

Usage

ConceptLattice$infimum(...)

Arguments

...

See Details.

Details

As argument, one can provide both integer indices or Concepts, separated by commas. The corresponding concepts are used to compute their infimum in the lattice.

Returns

The infimum of the list of concepts.

---

Method subconcepts()

Subconcepts of a Concept

Usage

ConceptLattice$subconcepts(C)

Arguments

C

(numeric or SparseConcept) The concept to which determine all its subconcepts.

Returns

A list with the subconcepts.

---

Method superconcepts()

Superconcepts of a Concept

Usage

ConceptLattice$superconcepts(C)

Arguments

C

(numeric or SparseConcept) The concept to which determine all its superconcepts.

Returns

A list with the superconcepts.

---

Method lower_neighbours()

Lower Neighbours of a Concept

Usage

ConceptLattice$lower_neighbours(C)

Arguments

C

(SparseConcept) The concept to which find its lower neighbours

Returns

A list with the lower neighbours of C.

---

Method upper_neighbours()

Upper Neighbours of a Concept

Usage

ConceptLattice$upper_neighbours(C)

Arguments

C

(SparseConcept) The concept to which find its upper neighbours

Returns

A list with the upper neighbours of C.

---

Method stability()

Computes the stability of each concept.

Usage

ConceptLattice$stability()

Returns

A numeric vector with the stability of each concept.

---

Method separation()

Computes the separation of each concept. Separation is the number of objects covered by the concept but not by any of its immediate subconcepts.

Usage

ConceptLattice$separation()

Returns

A numeric vector with the separation of each concept.

---

Method density()

Computes the fuzzy density of each concept.

Usage

ConceptLattice$density(I = NULL)

Arguments

I

(Optional) The original incidence matrix. If NULL, it tries to access it from the parent FormalContext if linked.

Returns

A numeric vector with the density of each concept.

---

Method check_properties()

Check algebraic properties of the lattice (Distributivity and Modularity).

Usage

ConceptLattice$check_properties()

Details

This method builds the adjacency matrix of the lattice order relation and calls an optimized C++ function to verify the properties.

Returns

A list with components distributive and modular (booleans).

---

Method is_distributive()

Check if the lattice is distributive. A lattice is distributive if \(x \wedge (y \vee z) = (x \wedge y) \vee (x \wedge z)\) for all elements.

Usage

ConceptLattice$is_distributive()

Returns

Logical.

---

Method is_modular()

Check if the lattice is modular. A lattice is modular if \(x \le z \implies x \vee (y \wedge z) = (x \vee y) \wedge z\). Distributive lattices are always modular.

Usage

ConceptLattice$is_modular()

Returns

Logical.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

ConceptLattice$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# Build a formal context
fc_planets <- FormalContext$new(planets)

# Find the concepts
fc_planets$find_concepts()

# Find join- and meet- irreducible elements
fc_planets$concepts$join_irreducibles()
#> A set of 5 concepts:
#> 1: ({Uranus, Neptune}, {medium, far, moon})
#> 2: ({Jupiter, Saturn}, {large, far, moon})
#> 3: ({Mercury, Venus}, {small, near, no_moon})
#> 4: ({Earth, Mars}, {small, near, moon})
#> 5: ({Pluto}, {small, far, moon})
fc_planets$concepts$meet_irreducibles()
#> A set of 7 concepts:
#> 1: ({Uranus, Neptune}, {medium, far, moon})
#> 2: ({Jupiter, Saturn}, {large, far, moon})
#> 3: ({Mercury, Venus}, {small, near, no_moon})
#> 4: ({Mercury, Venus, Earth, Mars}, {small, near})
#> 5: ({Mercury, Venus, Earth, Mars, Pluto}, {small})
#> 6: ({Jupiter, Saturn, Uranus, Neptune, Pluto}, {far, moon})
#> 7: ({Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto}, {moon})

# Get concept support
fc_planets$concepts$support()
#>  [1] 0.0000000 1.0000000 0.2222222 0.2222222 0.2222222 0.4444444 0.2222222
#>  [8] 0.5555556 0.1111111 0.3333333 0.5555556 0.7777778


## ------------------------------------------------
## Method `ConceptLattice$top`
## ------------------------------------------------

fc <- FormalContext$new(planets)
fc$find_concepts()
fc$concepts$top()
#> ({Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto}, {})


## ------------------------------------------------
## Method `ConceptLattice$bottom`
## ------------------------------------------------

fc <- FormalContext$new(planets)
fc$find_concepts()
fc$concepts$bottom()
#> ({}, {small, medium, large, near, far, moon, no_moon})