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Formal concept analysis: current trends and directions

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Abstract

Formalization of human thinking helps in fostering the process of learning by giving an explicit representation to human thoughts. Formal Concept Analysis (FCA) finds it’s core here. It considers a “concept” as a formal unit of human thought. A concept is represented as a set of inter related objects called the extent and the set of the properties of these objects, called the intent. Making use of the mathematical principles of Lattice Theory and Map Theory of Abstract Algebra, a set of tools and algorithms have been developed in FCA. These helps us to analyze and represent any context as a relation between it’s extent and intent. Concepts drawn from the subsets of the extent and intent can be organized in the form of a lattice giving a subsumption hierarchy. Such concept lattices could be maintained by different operations on the lattice like scaling, pruning, navigating etc. A host of applications and software have been developed over the years which serves the usage of FCA tools and processes for specific purposes in various fields. This paper reviews the theoretical foundation, research and applications of FCA in different areas. The paper projects current trends in FCA and concludes with a discussion on open issues and limitations of FCA.

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Notes

  1. Legends used in the formal context ‘Classes of sub-phylum Vertebrata of animalia kingdom’:

    Attributes: TER: Terrestial, ACQ: Aquatic, JAW: Jawed, HBLD: Hot-blooded, CBLD: Cold-blooded, FUR: Have fur, FLY: Flying, EGG: Egg-laying, MLK: Breast feeding, SHL: Shell on body, MSF: Muscular feet, PRS: Parasitic, BON: With bone

    Objects: AMP: Amphibian, RPT: Reptilian, AVS: Aves, PSC: Pisces, CYL: Cyclostomata, MML: Mammal, MRP: Marsipobranchia, LPT: Leptocardia

  2. In mathematical order theory, MEET and JOIN are two binary operations on a partially ordered set that respectively gives the supremum or Greatest Lower Bound and infimum or Lowest Upper Bound of their arguments, if they exist. MEET is denoted by \(\wedge \) and JOIN by \(\vee \).

  3. Legends used in the formal context ’Characteristics of species of Mammalia class’:

    • Attributes: DOM-Domesticated; DNT-Sharp denotation; ACQ-Lives in water; EGG-Egg laying; UGR-Underground; PRY-Preying; Objects: PLP-PLATYPUS(Ornithorhynchus anatinus); CHT-CHEETAH(Acinonyx jubatus); DLP-DOLPHIN; ROD-RODENT(Class RODENTIA); RBT-RABBIT(Order Lagomorpha);ELE-ELEPHANT (Family Elephantidae); HMN-HUMAN(Homo Sapiens); DOG-(Canis lupus familiaris);

  4. The Z notation, named after Zermelo-Fraenkel set theory, is a formal specification language used for describing and modeling computing systems. All expressions in Z notation are typed

  5. In the Table 4, ‘*’ represents the root of the noun. Inflectional paradigms are the set of affixes to a root word denoting the grammatical features of the root word

  6. Observational theory is a set of observational statements of the form \(\forall x|\upvarphi (\text{ x }) \rightarrow \uppsi (\text{ x })\) over a set of primitive predicates \(\Sigma \) such that \(\upvarphi , \Psi \in \text{ T } (\Sigma ), \text{ T } (\Sigma )\) being a free Algebra over \(\Sigma \)

  7. In Table 7, only abstracts of the papers marked * were accessible. ** is the seminal paper in German by Kipke and Wille on application of FCA to Semantics

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  1. Achyanta Kumar Sarmah

    Present address: Indian Institute of Management Shillong, Shillong, Meghalaya, India

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  1. Department of CSE, School of Engineering, Tezpur University, Tezpur, Assam, India

    Achyanta Kumar Sarmah, Shyamanta M. Hazarika & Smriti Kumar Sinha

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Sarmah, A.K., Hazarika, S.M. & Sinha, S.K. Formal concept analysis: current trends and directions. Artif Intell Rev 44, 47–86 (2015). https://doi.org/10.1007/s10462-013-9404-0

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