Computational approaches to concept formation often share a top-down, incremental, hill-climbing classification, and differ from each other in the concept representation and quality criteria. Each of them captures part of the rich variety of conceptual knowledge and many are well suited only when the object-attribute distribution is not sparse. Formal concept analysis is a set-theoretic model that mathematically formulates the human understanding of concepts, and investigates the algebraic structure, Galois lattice, of possible concepts in a given domain. Adopting the idea of representing concepts by mutual closed sets of objects and attributes as well as the Galois lattice structure for concepts from formal concept analysis, we propose an approach to concept formation and develop OSHAM, a method that forms concept hierarchies with high utility score, clear semantics and effective even with sparse object-attribute distributions. In this paper we describe OSHAM, and in an attempt to show its performance we present experimental studies on a number of data sets from the machine learning literature.

This paper gives a model to explain one phenomenon found in the process of creative concept formation, i.e. the phenomenon that people often get trapped in some state where the mental world remains nebulous and sometimes suddenly make a jump to a new concept. This phenomenon has been qualitatively explained mainly by the philosophers but there have not been models for explaining it quantitatively. Such model is necessary in a new research field to study the systems for aiding human creative activities. So far, the work on creation aid has not had theoretical background and the systems have been built based only on trial and error. The model given in this paper explains some aspects of the phenomena found in creative activities and give some suggestions for the future systems for aiding creative concept formation.