A comprehensive overview on the foundations of formal concept analysis

K. Sumangali ,Aswani Kumar Cherukuri

doi:10.34105/j.kmel.2017.09.032

Abstract

The immersion of voluminous collection of data is inevitable almost everywhere. The invention of mathematical models to analyse the patterns and trends of the data is an emerging necessity to extract and predict useful information in any Knowledge Discovery from Data (KDD) process. The Formal Concept Analysis (FCA) is an efficient mathematical model used in the process of KDD which is specially designed to portray the structure of the data in a context and depict the underlying patterns and hierarchies in it. Due to the huge increase in the application of FCA in various fields, the number of research and review articles on FCA has raised to a large extent. This review differs from the existing ones in presenting the comprehensive survey on the fundamentals of FCA in a compact and crisp manner to benefit the beginners and its focuses on the scalability issues in FCA. Further, we present the generic anatomy of FCA apart from its origin and growth at a primary level.

Highlights

The developments of information technologies and network have produced huge collection of data every year from different trades
Authors proposed a method that reduces the number of concepts using certain constraints, which are derived from attribute dependency formulas (ADF) that are inputted along with the formal context
In this paper we have presented an overview on the foundations of Formal Concept Analysis (FCA) and its historical growth to fulfil the thirst of the beginner towards FCA

Summary

Introduction

The developments of information technologies and network have produced huge collection of data every year from different trades. The invention of methods and means to automatically analyse the patterns and trends of the data is an emerging necessity in order to extract and predict useful information to the society (Malzahn, Ziebarth, & Hoppe, 2013; Mattingly, Rice, & Berge, 2012; Zushi, Miyazaki, & Norizuki, 2012). This is an important issue and apparently has high priority.

Origin and growth of FCA

Terms and notations in FCA

Formal context

Properties of concepts

Computation of concepts

Hierarchy of concepts

Concept lattices

Graphical representation of concept lattices

Many valued contexts and their scaling processes

Conceptual scaling

Attribute implications

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