Formal Concept Analysis

Formal concept analysis (FCA) is a principled way of deriving a concept hierarchy or formal ontology from a collection of objects and their properties. This means deriving implicit relationships between objects regarding their attributes.

Each concept in the hierarchy represents the set of objects sharing the same values for a certain set of properties; and each sub-concept in the hierarchy contains a subset of the objects in the concepts above it.

Formal concept analysis finds practical application in fields including data mining, text mining, machine learning or semantic web.

Building a FormalContext

We use the example from https://en.wikipedia.org/wiki/Formal_concept_analysis:

var fc = new FormalContext[Int, String]
fc.set_object_attributes(1, ["odd", "square"])
fc.set_object_attributes(2, ["even", "prime"])
fc.set_object_attributes(3, ["odd", "prime"])
fc.set_object_attributes(4, ["even", "composite", "square"])
fc.set_object_attributes(5, ["odd", "prime"])
fc.set_object_attributes(6, ["even", "composite"])
fc.set_object_attributes(7, ["odd", "prime"])
fc.set_object_attributes(8, ["even", "composite"])
fc.set_object_attributes(9, ["odd", "square", "composite"])
fc.set_object_attributes(10, ["even", "composite"])

Computing the set of FormalConcept

var concepts = fc.formal_concepts
for concept in concepts do
    print concept
end

Visualizing formal concept with ConceptLattice

var cl = new ConceptLattice[Int, String].from_concepts(concepts)
cl.show_dot