R6 class for a Bond Lattice

This class extends ConceptLattice to represent the lattice of bonds between two formal contexts \(K_1\) and \(K_2\). It inherits all lattice operations (finding irreducible elements, subconcepts, etc.) and provides specific methods to extract bonds as matrices and FormalContexts.

Super classes

fcaR::ConceptSet -> fcaR::ConceptLattice -> BondLattice

Public fields

elapsed

(numeric) Time elapsed during bond computation (C++ level)

Methods

Public methods

• BondLattice$new()

• BondLattice$get_bonds()

• BondLattice$similarity()

• BondLattice$get_core()

• BondLattice$print()

• BondLattice$is_bond()

• BondLattice$clone()

Inherited methods

• fcaR::ConceptSet$[()
• fcaR::ConceptSet$extents()
• fcaR::ConceptSet$intents()
• fcaR::ConceptSet$is_empty()
• fcaR::ConceptSet$size()
• fcaR::ConceptSet$sub()
• fcaR::ConceptSet$support()
• fcaR::ConceptSet$to_latex()
• fcaR::ConceptSet$to_list()
• fcaR::ConceptLattice$bottom()
• fcaR::ConceptLattice$decompose()
• fcaR::ConceptLattice$density()
• fcaR::ConceptLattice$dimension()
• fcaR::ConceptLattice$infimum()
• fcaR::ConceptLattice$is_atomic()
• fcaR::ConceptLattice$is_distributive()
• fcaR::ConceptLattice$is_modular()
• fcaR::ConceptLattice$is_semimodular()
• fcaR::ConceptLattice$join_irreducibles()
• fcaR::ConceptLattice$lower_neighbours()
• fcaR::ConceptLattice$meet_irreducibles()
• fcaR::ConceptLattice$plot()
• fcaR::ConceptLattice$separation()
• fcaR::ConceptLattice$set_state()
• fcaR::ConceptLattice$stability()
• fcaR::ConceptLattice$subconcepts()
• fcaR::ConceptLattice$sublattice()
• fcaR::ConceptLattice$superconcepts()
• fcaR::ConceptLattice$supremum()
• fcaR::ConceptLattice$to_json()
• fcaR::ConceptLattice$top()
• fcaR::ConceptLattice$upper_neighbours()
• fcaR::ConceptLattice$width()

---

Method new()

Initialize a BondLattice object.

Usage

BondLattice$new(extents, intents, objects, attributes, I, fc1, fc2)

Arguments

extents

(dgCMatrix) The extents of all concepts

intents

(dgCMatrix) The intents of all concepts

objects

(character) Names of the objects (not required for bonds, can be generic)

attributes

(character) Names of the attributes (flattened $G_1 \times M_2$)

I

(matrix) Built incidence matrix

fc1

(FormalContext) The first formal context

fc2

(FormalContext) The second formal context

Returns

A new BondLattice object.

---

Method get_bonds()

Extract the bonds represented by the intents of the lattice.

Usage

BondLattice$get_bonds(indices = NULL)

Arguments

indices

(numeric or logical vector) The indices of the bonds (concepts) to extract. If NULL (default), extracts all.

Returns

A list of FormalContext objects, each representing one bond.

---

Method similarity()

Compute similarity, affinity, or complexity metrics between the two contexts.

Usage

BondLattice$similarity(
  type = c("log-bond", "top-density", "complexity", "core-agreement", "entropy",
    "stability", "width", "dimension", "width-index", "dimension-index")
)

Arguments

type

(character) The type of metric to compute:

• "log-bond": (Default) Normalized log-ratio of bonds. High value means high logical affinity.

• "top-density": Density of the largest possible bond (the top of the lattice).

• "complexity": Ratio of irreducible bonds to total bonds. Low value implies high structural emergence.

• "core-agreement": Ratio of filled cells in the Core bond versus the Top bond. Measures fundamental consensus.

• "entropy": Interaction entropy based on the log-size of the lattices.

• "stability": Average stability of the bonds in the lattice.

Returns

A numeric value representing the metric.

---

Method get_core()

Get the 'Core' bond (the smallest possible bond).

Usage

BondLattice$get_core()

Returns

A FormalContext representing the minimal bond.

---

Method print()

Print the BondLattice object.

Usage

BondLattice$print()

Returns

Nothing, just prints the object summary.

---

Method is_bond()

Verify if a relation is a bond between the internal contexts.

Usage

BondLattice$is_bond(relation)

Arguments

relation

(matrix or FormalContext) The relation to verify.

Returns

TRUE if it's a bond, FALSE otherwise.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

BondLattice$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
set.seed(42)
mat1 <- matrix(sample(0:1, 15, replace = TRUE), nrow = 5, ncol = 3)
rownames(mat1) <- paste0("O", 1:5)
colnames(mat1) <- paste0("A", 1:3)
fc1 <- FormalContext$new(mat1)

mat2 <- matrix(sample(0:1, 12, replace = TRUE), nrow = 4, ncol = 3)
rownames(mat2) <- paste0("P", 1:4)
colnames(mat2) <- paste0("B", 1:3)
fc2 <- FormalContext$new(mat2)

bl <- bonds(fc1, fc2)

# Extract all bonds as FormalContext objects
my_bonds <- bl$get_bonds()
print(my_bonds[[1]])
#> FormalContext with 5 objects and 3 attributes.
#>     B1  B2  B3  
#>  O1             
#>  O2             
#>  O3             
#>  O4             
#>  O5             
# }