Exploration tools in formal concept analysis

The development of conceptual knowledge systems specifically requests knowledge acquisition tools within the framework of formal concept analysis. In this paper, the existing tools are presented, and furhter developments are discussed.

Concept exploration - a tool for creating and exploring conceptual hierarchies

Concept exploration is a knowledge acquisition tool for interactively exploring the hierarchical structure of finitely generated lattices. Applications comprise the support of knowledge engineers by constructing a type lattice for conceptual graphs, and the exploration of large formal contexts in formal concept analysis.

Hierarchies of conceptual scales

Formal Concept Analysis allows to derive conceptual hierarchies from data tables. Formal Concept Analysis is applied in various domains, e.g., data analysis, information retrieval, and knowledge discovery in databases. In order to deal with increasing sizes of the data tables (and to allow more complex data structures than just binary attributes), conceputal scales habe been developed. They are considered as metadata which structure the data conceptually. But in large applications, the number of conceptual scales increases as well. Techniques are needed which support the navigation of the user also on this meta-level of conceptual scales. In this paper, we attack this problem by extending the set of scales by hierarchically ordered higher level scales and by introducing a visualization technique called nested scaling. We extend the two-level architecture of Formal Concept Analysis (the data table plus one level of conceptual scales) to many-level architecture with a cascading system of conceptual scales. The approach also allows to use representation techniques of Formal Concept Analysis for the visualization of thesauri and ontologies.

Conceptual structures represented by conceptual graphs and formal concept analysis

Conceptual Graphs and Formal Concept Analysis have in common basic concerns: the focus on conceptual structures, the use of diagrams for supporting communication, the orientation by Peirce's Pragmatism, and the aim of representing and processing knowledge. These concerns open rich possibilities of interplay and integration. We discuss the philosophical foundations of both disciplines, and analyze their specific qualities. Based on this analysis, we discuss some possible approaches of interplay and integration.

A contextual-logic extension of TOSCANA

The aim of this paper is to indicate how TOSCANA may be extended to allow graphical representations not only of concept lattices but also of concept graphs in the sense of Contextual Logic. The contextual-logic extension of TOSCANA requires the logical scaling of conceptual and relatioal scales for which we propose the Peircean Algebraic Logic as reconstructed by R. W. Burch. As graphical representations we recommend, besides labelled line diagrams of concept lattices and Sowa's diagrams of conceptual graphs, particular information maps for utilizing background knowledge as much as possible. Our considerations are illustrated by a small information system about the domestic flights in Austria.

Fast computation of concept lattices using data mining techniques

We present a new algorithm called TITANIC for computing concept lattices. It is based on data mining techniques for computing frequent itemsets. The algorithm is experimentally evaluated and compared with B. Ganter's Next-Closure algorithm.

Conceptual knowledge discovery and data analysis

In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of empirically grounded theory building proposed by A. Strauss and J. Corbin.

Conceptual information systems discussed through an IT-security tool

Conceptual Information Systems are based on a formalization of the concept of "concept" as it is discussed in traditional philosophical logic. This formalization supports a human-centered approach to the development of Information Systems. We discuss this approach by means of an implemented Conceptual Information System for supporting IT security management in companies and organizations.

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.

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.