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Existing projection methods for data visualization use predefined criteria to choose the representation of data. There is a lack of methods that (i) use information on what the user 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 \u201cthis set of points forms a cluster\u201d, and requires no knowledge of maths. This background knowledge is used to find a maximum entropy distribution of the data, after which the user is provided with data projections for which the data and the maximum entropy distribution differ the most, hence showing the user aspects of data that are maximally informative given the background knowledge. We study the computational performance of our model and present use cases on synthetic and real data. 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