Visualization is used in data mining for visual presentation of already discovered patterns and for discovering new patterns visually. Success in both tasks depends on the ability of presenting abstract patterns as simple visual patterns. Getting simple visualizations for complex abstract patterns is an especially challenging problem. A new approach called inverse visualization (IV) is suggested to address the problem of visualizing complex patterns. The approach is based on specially designed data preprocessing. Preprocessed data permit the discovery of abstract patterns that can be presented by simple visual patterns. Design of data preprocessing transformations is based on a transformation theorem proved in the paper. A mathematical formalism is derived from the Representative Measurement Theory [Suppes at al, 1990] . The possibility of solving inverse visualization tasks is illustrated on functional non-linear additive dependencies φ(ƒ(x,z)). These dependencies are transformed into simple and intuitive visual patterns. The approach is called inverse visualization because it does not use data "as is" and does not follow a traditional sequence: discover pattern → visualize pattern. The new sequence is: convert data to visualizable form → discover patterns with predefined visualization.
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