Army

Visualization axis approach to presenting multivariate data sets

2D or 3D representation of 4D+ datasets that preserves the multivariate information and minimizes the dilution of information displayed

Without trying to offend Star Wars fans, the term “hyperspace” may have a more terrestrial meaning than that which plays out in a galaxy far, far away.

On earth, it is defined as the mathematical construct of a four or more dimensional space in contrast to a two- and three-dimensional space. Such datasets to be analyzed consist of points defined by four or more variables, (also referred to as multivariate data). The challenge in analyzing such datasets is that humans can only visualize 2D and 3D objects. With the exception of using time as the fourth dimension, humans cannot visualize multivariate datasets without some form of dimensional reduction, projection, mapping, or illustration tool that reduces the multivariate data to either a 2D or 3D form.

It is well known that a 2D object can be defined by the coordinates along two axes at right angles to each other and that a 3D object can be defined by the coordinates along three axes, each at right angles to the other two axes. Similarly, a 4D hyperspace object can be defined mathematically by four axes, each at right angles to the other three axes. As mentioned above, this 4D object or illustration cannot be visualized by a human, but it can be created in mathematical space. This hyperspace construct can be conceptualized in 3D as a constellation of points mapped within the visualized 3D points. That is, a point that can be visualized in 3D is assumed to represent a constellation of points in the fourth dimension. This conceptualization can be extended to any hyperspace dimension and therefore is not limited to 4D.

Army researchers have developed a novel process to display a hyperspace dataset that surpasses current methods including principal component analysis (PCA) and dendrograms. The approach utilizes a maximum-distance means to generate axes for dimensional reduction in such a way that preserves the relative angle information from each point in the dataset, thus providing the capability to produce a more picture-like image for human viewing.