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 \(\alpha : \mathcal{O}\mapsto \mathcal{A}\) and \(\beta : \mathcal{A}\mapsto \mathcal{O}\) are defined so that the operator α(O)...
Recommended Reading
Carpineto, C., & Romano, G. (2004). Concept data analysis. Theory and applications. New York: Wiley.
Davey, B. A., & Priestly, H. A. (2002). Introduction to lattices and order. Cambridge: Cambridge University Press.
Ganter, B. & Wille, R. (1998). Formal concept analysis. Mathematical foundations. Heidelberg: Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this entry
Cite this entry
Garriga, G.C. (2011). Formal Concept Analysis. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_316
Download citation
DOI: https://doi.org/10.1007/978-0-387-30164-8_316
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30768-8
Online ISBN: 978-0-387-30164-8
eBook Packages: Computer ScienceReference Module Computer Science and Engineering