Visual exploration of high-dimensional real-valued datasets is a fundamental task in exploratory data analysis (EDA). Existing methods use predefined criteria to choose the representation of data. There is a lack of methods that (i) elicit from the user what she has learned from the data and (ii) show patterns that she does not know yet. We construct a theoretical model where identified patterns can be input as knowledge to the system. The knowledge syntax here is intuitive, such as "this set of points forms a cluster", and requires no knowledge of maths. This background knowledge is used to find a Maximum Entropy distribution of the data, after which the system provides the user data projections in which the data and the Maximum Entropy distribution differ the most, hence showing the user aspects of the data that are maximally informative given the user's current knowledge. We provide an open source EDA system with tailored interactive visualizations to demonstrate these concepts. We study the performance of the system and present use cases on both synthetic and real data. We find that the model and the prototype system allow the user to learn information efficiently from various data sources and the system works sufficiently fast in practice. We conclude that the information theoretic approach to exploratory data analysis where patterns observed by a user are formalized as constraints provides a principled, intuitive, and efficient basis for constructing an EDA system.
The system presented here can be also considered to be an instance of visually controllable data mining @cite_28 , where the objective is to implement advanced data analysis methods understandable and efficiently controllable by the user. Our approach satisfies the properties of a visually controllable data mining method (see @cite_28 , Sec. II B): (VC1) the data and model space are presented visually, (VC2) there are intuitive visual interactions allowing the user to modify the model space, and (VC3) the method is fast enough for visual interaction.
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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 mining perspective, this work creates a reference framework for, designing and evaluating visually controllable algorithms and visual analytics systems.