Building taxonomies is often a significant part of building an ontology, and many attempts have been made to automate the creation of such taxonomies from relevant data. The idea in such approaches is either that relevant definitions of the intension of concepts can be extracted as patterns in the data (e.g. in formal concept analysis) or that their extension can be built from grouping data objects based on similarity (clustering). In both cases, the process leads to an automatically constructed structure, which can either be too coarse and lacking in definition, or too fined-grained and detailed, therefore requiring to be refined into the desired taxonomy. In this paper, we explore a method that takes inspiration from both approaches in an iterative and interactive process, so that refinement and definition of the concepts in the taxonomy occur at the time of identifying those concepts in the data. We show that this method is applicable on a variety of data sources and leads to taxonomies that can be more directly integrated into ontologies.