A new metaphor for projection-based visual analysis and data exploration

In many important application domains such as Business and Finance, Process Monitoring, and Security, huge and quickly increasing volumes of complex data are collected. Strong efforts are underway developing automatic and interactive analysis tools for mining useful information from these data repositories. Many data analysis algorithms require an appropriate definition of similarity (or distance) between data instances to allow meaningful clustering, classification, and retrieval, among other analysis tasks. Projection-based data visualization is highly interesting (a) for visual discrimination analysis of a data set within a given similarity definition, and (b) for comparative analysis of similarity characteristics of a given data set represented by different similarity definitions. We introduce an intuitive and effective novel approach for projection-based similarity visualization for interactive discrimination analysis, data exploration, and visual evaluation of metric space effectiveness. The approach is based on the convex hull metaphor for visually aggregating sets of points in projected space, and it can be used with a variety of different projection techniques. The effectiveness of the approach is demonstrated by application on two well-known data sets. Statistical evidence supporting the validity of the hull metaphor is presented. We advocate the hull-based approach over the standard symbol-based approach to projection visualization, as it allows a more effective perception of similarity relationships and class distribution characteristics.