Techniques for precision-based visual analysis of projected data

The analysis of high-dimensional data is an important, yet inherently difficult problem. Projection techniques such as PCA, MDS, and SOM can be used to map high-dimensional data to 2D display space. However, projections typically incur a loss in information. Often uncertainty exists regarding the precision of the projection as compared with its original data characteristics. While the output quality of these projection techniques can be discussed in terms of algorithmic assessment, visualization is often helpful for better understanding the results. We address the visual assessment of projection precision by an approach integrating an appropriately designed projection precision measure directly into the projection visualization. To this end, a flexible projection precision measure is defined that allows the user to balance the degree of locality at which the measure is evaluated. Several visual mappings are designed for integrating the precision measure into the projection visualization at various levels of abstraction. The techniques are implemented in a fully interactive system which is practically applied on several data sets. We demonstrate the usefulness of the approach for visual analysis of classified and clustered high-dimensional data sets. We thereby show how our novel interactive precision quality visualization system helps to examine preservation of closeness of the data in original space into the low-dimensional space.