Impact of local congruences in variable selection from datasets

TL;DR

This paper investigates how local congruences influence attribute reduction in formal concept analysis, focusing on understanding the modifications to datasets and their impact on concept lattices.

Contribution

It introduces a method to analyze the effects of local congruences on attribute reduction and dataset modifications within FCA.

Findings

Local congruences can significantly alter attribute reduction results.

Understanding dataset modifications helps interpret the impact of local congruences.

The approach aids in obtaining more robust concept clusters.

Abstract

Formal concept analysis (FCA) is a useful mathematical tool for obtaining information from relational datasets. One of the most interesting research goals in FCA is the selection of the most representative variables of the dataset, which is called attribute reduction. Recently, the attribute reduction mechanism has been complemented with the use of local congruences in order to obtain robust clusters of concepts, which form convex sublattices of the original concept lattice. Since the application of such local congruences modifies the quotient set associated with the attribute reduction, it is fundamental to know how the original context (attributes, objects and relationship) has been modified in order to understand the impact of the application of the local congruence in the attribute reduction.