Many visualization techniques involve mapping high-dimensional data spaces to lower-dimensional views. Unfortunately, mapping a high-dimensional data space into a scatterplot involves a loss of information; or, even worse, it can give a misleading picture of valuable structure in higher dimensions. In this paper, we propose class consistency as a measure of the quality of the mapping. Class consistency enforces the constraint that classes of n-D data are shown clearly in 2-D scatterplots. We propose two quantitative measures of class consistency, one based on the distance to the class's center of gravity, and another based on the entropies of the spatial distributions of classes. We performed an experiment where users choose good views, and show that class consistency has good precision and recall. We also evaluate both consistency measures over a range of data sets and show that these measures are efficient and robust.

Visualization techniques often use color to present categorical differences to a user. When selecting a color palette, the perceptual qualities of color need careful consideration. Large coherent groups visually suppress smaller groups and are often visually dominant in images. This paper introduces the concept of class visibility used to quantitatively measure the utility of a color palette to present coherent categorical structure to the user. We present a color optimization algorithm based on our class visibility metric to make categorical differences clearly visible to the user. We performed two user experiments on user preference and visual search to validate our visibility measure over a range of color palettes. The results indicate that visibility is a robust measure, and our color optimization can increase the effectiveness of categorical data visualizations.

During the last two decades a wide variety of advanced methods for the Visual Exploration of large data sets have been proposed. For most of these techniques user interaction has become a crucial element, since there are many situations in which an user or an analyst has to select the right parameter settings from among many or select a subset of the available attribute space for the visualization process, in order to construct valuable visualizations that provide insight into the data and reveal interesting patterns. The right choice of input parameters is often essential, since suboptimal parameter settings or the investigation of irrelevant data dimensions make the exploration process more time consuming and may result in wrong conclusions. In this paper we propose a novel method for automatically determining meaningful parameter-and attribute settings based on the Information content of the resulting visualizations.Our technique called Pixnostics, in analogy to Scagnostics[1] automatically analyses pixel images resulting from diverse parameter mappings and ranks them according to the potential value for the user. This allows a more effective and more efficient visual data analysis process, since the attribute/parameter space is reduced to meaningful selections and thus the analyst obtains faster insight into the data. Real world applications are provided to show the benefit of the proposed approach.

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