Mining minimal non-redundant association rules using frequent closed itemsets

The problem of the relevance and the usefulness of extracted association rules is of primary importance because, in the majority of cases, real-life databases lead to several thousands association rules with high confidence and among which are many redundancies. Using the closure of the Galois connection, we define two new bases for association rules which union is a generating set for all valid association rules with support and confidence. These bases are characterized using frequent closed itemsets and their generators; they consist of the non-redundant exact and approximate association rules having minimal antecedents and maximal consequences, i.e. the most relevant association rules. Algorithms for extracting these bases are presented and results of experiments carried out on real-life databases show that the proposed bases are useful, and that their generation is not time consuming.

Intelligent structuring and reducing of association rules with formal concept analysis

Association rules are used to investigate large databases. The analyst is usually confronted with large lists of such rules and has to find the most relevant ones for his purpose. Based on results about knowledge representation within the theoretical framework of Formal Concept Analysis, we present relatively small bases for association rules from which all rules can be deduced. We also provide algorithms for their calculation.

Mining association rules in folksonomies

Social bookmark tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. These systems provide currently relatively few structure. We discuss in this paper, how association rule mining can be adopted to analyze and structure folksonomies, and how the results can be used for ontology learning and supporting emergent semantics. We demonstrate our approach on a large scale dataset stemming from an online system.

Efficient mining of association rules based on formal concept analysis

Association rules are a popular knowledge discovery technique for warehouse basket analysis. They indicate which items of the warehouse are frequently bought together. The problem of association rule mining has first been stated in 1993. Five years later, several research groups discovered that this problem has a strong connection to Formal Concept Analysis (FCA). In this survey, we will first introduce some basic ideas of this connection along a specific algorithm, TITANIC, and show how FCA helps in reducing the number of resulting rules without loss of information, before giving a general overview over the history and state of the art of applying FCA for association rule mining.

Conceptual knowledge discovery with frequent concept lattices

Knowledge discovery support environments include beside classical data analysis tools also data mining tools. For supporting both kinds of tools, a unified knowledge representation is needed. We show that concept lattices which are used as knowledge representation in Conceptual Information Systems can also be used for structuring the results of mining association rules. Vice versa, we use ideas of association rules for reducing the complexity of the visualization of Conceptual Information Systems.

Efficient data mining based on formal concept analysis

Formal Concept Analysis is an unsupervised learning technique for conceptual clustering. We introduce the notion of iceberg concept lattices and show their use in Knowledge Discovery in Databases (KDD). Iceberg lattices are designed for analyzing very large databases. In particular they serve as a condensed representation of frequent patterns as known from association rule mining. In order to show the interplay between Formal Concept Analysis and association rule mining, we discuss the algorithm TITANIC. We show that iceberg concept lattices are a starting point for computing condensed sets of association rules without loss of information, and are a visualization method for the resulting rules.

Off to new shores

In the last years, the main orientation of Formal Concept Analysis (FCA) has turned from mathematics towards computer science. This article provides a review of this new orientation and analyzes why and how FCA and computer science attracted each other. It discusses FCA as a knowledge representation formalism using five knowledge representation principles provided by Davis, Shrobe, and Szolovits [DSS93]. It then studies how and why mathematics-based researchers got attracted by computer science. We will argue for continuing this trend by integrating the two research areas FCA and Ontology Engineering. The second part of the article discusses three lines of research which witness the new orientation of Formal Concept Analysis: FCA as a conceptual clustering technique and its application for supporting the merging of ontologies; the efficient computation of association rules and the structuring of the results; and the visualization and management of conceptual hierarchies and ontologies including its application in an email management system.

Iceberg query lattices for datalog

In this paper we study two orthogonal extensions of the classical data mining problem of mining association rules, and show how they naturally interact. The first is the extension from a propositional representation to datalog, and the second is the condensed representation of frequent itemsets by means of Formal Concept Analysis (FCA). We combine the notion of frequent datalog queries with iceberg concept lattices (also called closed itemsets) of FCA and introduce two kinds of iceberg query lattices as condensed representations of frequent datalog queries. We demonstrate that iceberg query lattices provide a natural way to visualize relational association rules in a non-redundant way.