Definition
Formal concept analysis is a mathematical theory of concept hierarchies that builds on order theory; it can be seen as an unsupervised machine learning technique and is typically used as a method of knowledge representation. The approach takes an input binary relation (binary matrix) specifying a set of objects (rows) and a set of attributes for those objects (columns), finds the natural concepts described in the data, and then organizes the concepts in a partial order structure or Hasse diagram. Each concept in the final diagram is a pair of sets of objects and attributes that are maximally contained one in each other.
Theory
The above intuition can be formalized through a Galois connection as follows. Let R be the binary relation between a set of objects and a set of attributes, that is, \(R \subseteq \mathcal{O}\times \mathcal{A}\). Two mappings α: \(\mathcal{O}\mapsto \mathcal{A}\) and β: \(\mathcal{A}\mapsto \mathcal{O}\) are defined so that the operator α(O), for some \...
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Recommended Reading
Carpineto C, Romano G (2004) Concept data analysis. Theory and applications. Wiley, New York
Davey BA, Priestly HA (2002) Introduction to lattices and order. Cambridge University Press, Cambridge
Ganter B, Wille R (1998) Formal concept analysis. Mathematical foundations. Springer, Heidelberg
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Garriga, G.C. (2017). Formal Concept Analysis. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_316
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DOI: https://doi.org/10.1007/978-1-4899-7687-1_316
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Publisher Name: Springer, Boston, MA
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