The Galois (or concept) lattice produced from a binary relation has proved useful for many applications. Building the Galois lattice can be considered a conceptual clustering method because it results in aconcept 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 update is done in time proportional to the number of instances previously treated. Although the worst case is exponential, when there is a fixed upper bound on the number of features related to an instance, which is usually the case in practical applications. the worst-case analysis of the algorithm also shows linear growth with respect to the number of instances.

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Building and maintaining the class hierarchy has been recognized as an important but one of the most difficult activities of object‐oriented design. Concept (or Galois) lattices and related structures are presented as a framework for dealing with the design and maintenance of class hierarchies. Because the design of class hierarchies is inherently an iterative and incremental process, we designed incremental algorithms that update existing Galois lattices as the result of adding, removing, or modifying class specifications. A prototype tool incorporating this and other algorithms has been developed as part of the IGLOO project, which is a large object‐oriented software engineering joint research project involving academic and industrial partners. The tool can generate either the concept lattice or several variant structures incrementally by incorporating new classes one by one. The resulting hierarchies can be interactively explored and refined using a graphical browser. In addition, several metrics are computed to help evaluating the quality of the hierarchies. Experiments are presented to better assess the applicability of the approach. © 1998 John Wiley & Sons, Inc.