An Intuitive Approach to Visualize Multidimensional Data and Relationships
Gautam Agrawal, Christina Bloebaum · 44th AIAA Aerospace Sciences Meeting and Exhibit · 2006
Multidimensional relationships exist in almost any discipline. There are numerous visualization methods that enable us to ‘see’ multidimensional relationships in an easy and intuitive manner for two or three variables, using 2-d and 3-d representation s. It is substantially more difficult, and sometimes even impossible, to visualize more than three dimensions – at least easily or in a way that is intuitive to the user. In this paper, a visualization methodology is presented in which multidimensional relationships can be viewed in an intuitive and straightforward manner. Based on this visualization, it is possible to quickly identify regions of interest for functional relationships, optimization applications, or for high dimensional datasets, regardless of the complexity of space or data. The technology provides a new approach to visualize more than three dimensions in a way that looks remarkably similar to traditional 2-d and 3-d representations. The method uses a new technique of ‘lossless’ dimension blending, termed the Hyper-Space Diagonal Counting (HSDC). The methodology developed here provides a unique way to visually represent the relationships for n-dimensional problems. What is described here represents a totally new methodology that has the potential to greatly impact numerous industries, as well as th e educational enterprise.