Algebraic operators for querying pattern bases

TL;DR

This paper introduces algebraic operators within formal concept analysis to improve pattern manipulation, enrichment, and approximation, facilitating more flexible pattern discovery and management in data analysis.

Contribution

It defines novel algebraic operators for patterns in FCA, enabling manipulation, updating, and approximation of concept sets in response to data and user needs.

Findings

Operators formalize pattern manipulation in FCA

Enables dynamic updating of pattern sets

Supports approximation of concepts using related patterns

Abstract

The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and updating a pattern set (e.g., concepts, rules) when changes occur in the user's needs and the input data (e.g., object/attribute insertion or elimination, taxonomy utilization), and (iii) approximate a "presumed" concept using a related pattern space so that patterns can augment data with knowledge. To conduct our work, we use formal concept analysis (FCA) as a framework for pattern discovery and management and we take a joint database-FCA perspective by defining operators similar in spirit to relational algebra operators, investigating approximation in concept lattices and exploiting existing work related to operations on contexts and lattices to formalize such operators.