Formal Concept Analysis with Constraints by EM Operators

Hua Mao

doi:10.22342/jims.23.1.197.13-26

Abstract

Formal concept analysis is a method of exploratory data analysisthat aims at the extraction of natural cluster from object-attributedata tables. We present a way to add user's background knowledge toformal concept analysis. The type of background knowledge we dealwith relates to relative importance of attributes in the input data.We introduce EM operators which constrain in attributes of formalconcept analysis. The main aim is to make extraction of conceptsfrom the input data more focused by taking into account thebackground knowledge. Particularly, only concepts which arecompatible with the constraint are extracted from data. Therefore,the number of extracted concepts becomes smaller since we leave outnon-interesting concepts. We concentrate on foundational aspectssuch as mathematical feasibility and computational tractability.

Highlights

Formal concept analysis (FCA) is a method of data analysis and visualization which deals with input data in the form of a table describing objects, their attributes, and their relationship
As [8] points, FCA is proved to be useful for knowledge extraction form and visualization of binary data-sets in various application domains such as organization of Web search results into a hierarchical structure of concepts based on common topics, information retrieval, and so on
The authors [6] indicate that a distinguishing feature of FCA is an inherent integration of three components: discovery of clusters in data, discovery of data dependencies in data, and visualization of formal concepts and attribute implications by a single hierarchical diagram

Summary

Introduction

Formal concept analysis (FCA) is a method of data analysis and visualization which deals with input data in the form of a table describing objects, their attributes, and their relationship (cf. [10] and [12]). As [8] points, FCA is proved to be useful for knowledge extraction form and visualization of binary data-sets in various application domains such as organization of Web search results into a hierarchical structure of concepts based on common topics, information retrieval, and so on (see [8,9,10, 12,13,14,15,16,17]). It is often the case that there is an additional information available in the form of a constraint (requirement) specified by a user In such a case, one is not interested in all the outputs but only in those which satisfy the constraint. To find a simpler operator than a closure operator to constraint on input data is always the pursue of researchers, since the pursued result will lead to a wider application of FCA.

Preliminaries

Constrained Attributes

Conclusions