The focus of this dissertation is to develop an algorithmic approach to the evaluation of visual retrieval in 3D from document databases represented as multidimensional vector spaces. We are presenting the Uexküll approach, which entails the representation of document databases as multidimensional vector spaces. From such a space 3D projections are selected and downloaded by users. A downloaded projection is defined by three named axes, and it presents documents (possibly also index terms) that pertain to these axes as objects of some form, e.g. droplets, in a 3D scene. Users may navigate among these objects in relation to the axes, scrutinizing and retrieving documents of interest. The evaluation approach is purely algorithmic. The aim is to evaluate the ability of a multidimensional vector space (termed a data organization) to facilitate the visual retrieval of relevant documents, placing such documents prominently along coordinate axes of downloaded projections. The evaluation approach is based on the Cranfield evaluation model, transforming the retrieved projection into a ranked list of documents. The Cranfield model is augmented with measures that gauge aspects of usability that are important for successful retrieval within an Uexküll environment. These aspects are the visibility of relevant documents and the separation of such documents from the non-relevant ones.

The presented evaluation approach is applied to data organizations of varying dimensionalities based on the singular value decomposition (SVD), rotated both orthogonally and obliquely, showing the effect of rotation and dimensionality on the quality of the data organization and the extent to which it facilitates Uexküll-based retrieval.