Informative Data Projections: A Framework and Two Examples

Projection Pursuit aims to facilitate visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge in Projection Pursuit is the design of a projection index—a suitable quality measure to maximise. We introduce a strategy for tackling this problem based on quantifying the amount of information a projection conveys, given a user’s prior beliefs about the data. The resulting projection index is a subjective quantity, explicitly dependent on the intended user. As an illustration, we developed this principle for two kinds of prior beliefs; the first leads to PCA, the second leads to a novel projection index, which we call t-PCA, that can be regarded as a robust PCA-variant. We demonstrate t-PCA’s usefulness in comparative experiments against PCA and FastICA, a popular PP method.