Extending the dimensionality of flatland with attribute view probabilistic models

In much of Bertin's Semiology of Graphics , marks representing individuals are arranged on paper according to their various attributes (components). Paper and computer monitors can conveniently map two attributes to width and height, and can map other attributes into nonspatial dimensions such as texture, or colour. Good visualizations exploit the human perceptual apparatus so that key relationships are quickly detected as interesting patterns. Graphical models take a somewhat dual approach with respect to the original information. Components, rather than individuals, are represented as marks. Links between marks represent conceptually simple, easily computable, and typically probabilistic relationships of possibly varying strength, and the viewer studies the diagram to discover deeper relationships. Although visually annotated graphical models have been around for almost a century, they have not been widely used. We argue that they have the potential to represent multivariate data as generically as pie charts represent univariate data. The present work suggests a semiology for graphical models, and discusses the consequences for information visualization.