Faithful Visualisation of Similarities in High Dimensional Data

In the last fifteen years, new methods of dimension reduction have been invented that enable much improved visualisation of high-dimensional data-sets. Conventionally, the data-sets are visualised as two-dimensional scatterplots, and similarity relationships between data-cases are revealed by grouping and proximity of points in the plane. But the arrangement of points in a 2D scatterplot cannot faithfully represent complex high-dimensional structure: more expressive 2D visualisations are needed.

This thesis develops new types of diagram that can represent data-similarities more expres- sively than a mere scatterplot. The approach is to automatically select a graph to overlay on the scatterplot, in order to enable a richer visualisation of similarities than is possible by the arrangement of points alone, and to correct distortions inherent in scatterplot visualisation.

Methods and software are developed for selecting and graphically representing the overlay graph as a diagram that humans can read. These diagrams enable correct and informative human interpretation of scatterplots that would otherwise be hard to interpret or misleading.