A large number of data mining methods are, as such, not applicable to fast, intuitive, and interactive use. Thus, there is a need for visually controllable data mining methods. Such methods should comply with three major requirements: their model structure can be represented visually, they can be controlled using visual interaction, and they should be fast enough for visual interaction. We define a framework for using data mining methods in interactive visualization. These data mining methods are called "visually controllable" and combine data mining with visualization and user-interaction, bridging the gap between data mining and visual analytics. Our main objective is to define the interactive visualization scenario and the requirements for visually controllable data mining. Basic data mining algorithms are reviewed and it is demonstrated how they can be controlled visually. We also discuss how existing visual analytics tools fit to the proposed framework. From a data minin...