Gaining understanding of multivariate and multidimensional data through visualization

High dimensionality is a major challenge for data visualization. Parameter optimization problems require an understanding of the behaviour of the objective function in the n-dimensional space around the optimum—this is multidimensional visualization and is the traditional domain of scientific visualization. Large data tables require us to understand the relationship between attributes in the table—this is multivariate visualization and is an important aspect of information visualization. Common to both types of ‘high-dimensional’ visualization is a need to reduce the dimensionality for display. In this paper we present a uniform approach to the filtering of both multidimensional and multivariate data, to allow extraction of data subject to constraints on their position or value within an n-dimensional window, and on choice of dimensions for display. A simple example of understanding the trajectory of solutions from an optimization algorithm is given—this involves a combination of multidimensional and multivariate data.