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Glossary.md

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Basics of FCA

  • Object: An index of a row in the data

  • Attribute: An index of a (binary) column in the data

  • Formal Context: A binary dataset represented as a triplet of objects, attributes and their connections

  • Description: A subset of attributes

  • Extent: The maximal subset of objects described by some description

  • Intent: The maximal subset of attributes describing some objects. Also, the maximal subset of attributes describing the same objects as some given description.

  • Concept: A pair of corresponding extent and intent, so a pair of a maximal subset of objects and their maximal description.

  • Concept Lattice: A set of all concepts in the data ordered by generality

  • Order on concepts: Concepts are ordered by their generality. So concept A is less than concept B if A is less general than B. That is, if B covers all the objects from A, or if A contains all the attributes from B.

  • Sub concepts: All concepts that are less general than some given concept

  • Super concepts: All concepts that are more general than some given concept

  • Previous concepts: The most general sub concepts

  • Next concepts: The least general super concepts

Minimal descriptions

  • Key: A minimal subset of attributes describing some objects (there may be many keys for the same subset of objects)
  • Passkey: A shortest subset of attributes describing some objects (there may be many passkeys for the same subset of objects)

Implications

  • Premise: The left part of implication A => B, so the condition of the implication

  • Conclusion: The right part of implication A => B, so what is implied by the implication

  • Saturation: The process of enriching a description with a given set of implications. For example, given description {color_is_green} and implications {} => {fruit}, {fruit, color_is_green} => {form_is_oval}, description {color_is_green} can be saturated into description {color_is_green, fruit}, because everything implies {fruit}, And then description {color_is_green, fruit} can be saturated into {color_is_green, fruit, form_is_oval} based on the second given implication.

  • Proper Premise: A description that implies some attributes, not implied by its subdescriptions.

  • Pseudo-intent: A description that implies some attributes, not implied by its subdescriptions and saturated w.r.t. the other pseudo-intents.

  • Canonical Direct basis (also Proper Premise basis or Karell basis): A set of implications where every premise is a proper premise. Such set of implication is direct, that is one can saturate a description passing every implication only once.

  • Canonical basis (also Pseudo-intent basis or Duquenne-Guiges basis): A set of implications where every premise is a pseudo-intent. Such set of implication is the smallest possible set of implications covering all the implications in the data.

  • Unit basis: A set of implications where every conclusion is a single attribute and not a subset of attributes.

Interestingness measures

  • Support: The number of objects described by a description (or concept, or implication). In caspailleur the term "support" is synonymous to "frequency" which is the percentage of objects described by a description.
  • Delta-stability: The minimal number of objects a description will lose if added at least one other attribute.