. The Galois (or concept) lattice produced from a binary relation has been proved useful for many applications. Building the Galois lattice can be considered as a conceptual clustering method since it results in a concept hierarchy. This article presents incremental algorithms for updating the Galois lattice and corresponding graph, resulting in an incremental concept formation method. Different strategies are considered based on a characterization of the modifications implied by such an update. Results of empirical tests are given in order to compare the performance of the incremental algorithms to three other batch algorithms. Surprisingly, when the total time for incremental generation is used, the simplest and less efficient variant of the incremental algorithms outperforms the batch algorithms in most cases. When only the incremental update time is used, the incremental algorithm outperforms all the batch algorithms. Empirical evidence shows that, on the average, the incremental u...

. 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...

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. Logical scaling is a new method to transform data matrices which are based on object-attribute-value-relationships into data matrices from which conceptual hierarchies can be explored. The derivation of concept lattices is determined by terminologies expressed in a formallogical language. Published in: D. Lukose et.al. (eds.): Conceptual Structures: Fulfilling Peirce's Dream. Proceedings of the ICCS'97, LNAI 1257, Springer, Berlin 1997, 332--341. 1 Introduction The aim of formal concept analysis is to explore conceptual patterns in empirical data contexts. Methods have been developed to find conceptual hierachies and to represent them in line diagrams based on concept lattices (cf. [Wi82], [GW96]). These methods can be of great interest for knowledge representation and data mining. Concept lattices can also be relevant as principled ways to structure the type lattices used for conceptual graphs. In general, there is no immediate, "automatic" way to derive the conceptual structures o...

The aim of this paper is to contribute to Data Analysis by clarifying how concept graphs may be derived from data tables. First it is shown how, by the method of relational scaling, a many-valued data context can be transformed into a power context family. Then it is proved that the concept graphs of a power context family form a lattice which can be described as a subdirect product of specific intervals of the concept lattices of the power context family (each extended by a new top-element). How this may become practical is demonstrated using a data table about the domestic flights in Austria. Finally, the lattice of syntactic concept graphs over an alphabet of object, concept, and relation names is determined and related to the lattices of concept graphs of the power context families which are semantic models of the given contextual syntax.

Abstract: Ripple down rules have addressed two of the major limitations of first generation Expert Systems (ES), the maintenance and knowledge acquisition (KA) bottleneck problems. This is achieved through acquiring knowledge directly from an expert, the use of an exception structure for knowledge representation and the storing of the cornerstone case associated with each rule. Just as RDR has offered a paradigm shift in the way these problems were solved, it is expected that RDR can offer a new approach to the issue of knowledge reuse. Due the poor acceptance of ES by end-users, our focus is more on reusing knowledge in different modes, such as explanation, critiquing or ‘what-if ’ within the same domain rather than the more conventional approach of reusing problem-solving methods or ontologies to solve a similar problem in a somewhat differerent domain. An evaluation of RDR for reuse showed that many modes of use were possible without any change to the knowledge or its structure but that some modes required understanding of the models represented. Since RDR does not require analysis or modeling of the domain for KA, maintenance or finding conclusions we have incorporated ideas from Formal Concept Analysis (FCA) to allow concepts and the relationships between them to be identified and explored. The addition of FCA tools to RDR is described in this paper. 1. The Reuse of Knowledge The reuse of knowledge should result in potential savings

Abstract. For over a decade, work on Formal Concept Analysis has been accompanied by the development of the Toscana software. Toscana was implemented to realize the idea of Conceptual Information Systems which allow the analysis of data using concept-oriented methods. Over the years, many ideas from Formal Concept Analysis have been tested in Toscana systems while the real-world problems encountered led to new theoretical research. After ten years of development, the ToscanaJ project was initiated to solve some outstanding problems of the older Toscana versions. The ToscanaJ suite provides programs for creating and using Conceptual Information Systems. The experience with older Toscana implementations has been applied to the design of the programs. A workflow that developed through many Toscana projects has now been integrated into the tools to make them easier to use. Implemented as an Open-Source project and embedded into the larger Tockit project, ToscanaJ is also a starting point for creating a common base for software development for Formal Concept Analysis. In this paper, we present the features of the ToscanaJ suite and how they can be used to implement Conceptual Information Systems. 1

Due to the rapid growth of the World-Wide Web, resource discovery has become an increasing problem. As an answer to the demand for information management, a third generation of World-Wide Web tools will evolve: information gathering and processing agents. This paper describes wave (Web Analysis and Visualization Environment), a 3D interface for World-Wide Web information visualization and browsing. It uses the mathematical theory of concept analysis to conceptually cluster objects. So-called "conceptual scales" for attributes, such as location, title, keywords, topic, size, or modification time, provide a formal mechanism that automatically classifies and categorizes documents, creating a conceptual information space. A visualization shell serves as an ergonomically sound user interface for exploring this information space. 1 Introduction The World-Wide Web has gained its amazing popularity through the availability of "point and shoot" browsing tools like Mosaic. They provide access ...

Common clustering techniques have the disadvantage that they do not provide intensional descriptions of the clusters obtained. Conceptual Clustering techniques, on the other hand, provide such descriptions, but are known to be rather slow. In this paper, we discuss a way of combining both techniques. We first cluster the documents by a variant of #--Means, using a thesaurus as background knowledge. This clustering reduces the large number of documents to a relatively small number of clusters, which can then be clustered conceptually in the second step.

The work reported in this thesis is motivated by the belief that knowledge-based systems (KBS) research needs to focus more on users ’ needs and cater for the various decision situations in which users will find themselves. To build individual systems that cater for all the activities that may be needed is not feasible or desirable. The problems associated with capturing knowledge are well known and the ability to capture knowledge once and access and manipulate the knowledge in multiple ways is highly desirable. It adds value to the original knowledge and offers all the benefits associated with the reuse of resources. Thus, the problem becomes one of knowledge reuse. The research question pursued in this thesis is “can knowledge captured for one purpose, such as consultation, be reused to support a wide range of alternative purposes, such as critquing or tutoring, allowing the user to answer different types of questions according to their current circumstances”? Further, this question was to be answered in a situated cognition, dynamic knowledge framework. The system developed in this thesis is based on the Multiple Classification Ripple Down Rule (MCRDR) knowledge acquisition and representation technique. MCRDR is a form of casedbased