Statistical and computational methodology for visualizing high-dimensional digital data

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Canadians have access to enormous numbers of digital data objects in the form of documents, web sites, images, sound, and video. A set of instances of any one of these forms may be represented as a set of data points in a high-dimensional space (possibly 10s or 100s or 1000s of dimensions); the structure of the relative positions of these points in the space matches conceptual relationships between the original objects. The proposed research is directed towards the development of statistical methodology and software which will allow one to meaningfully explore any such collection by presenting it visually as a sequence of low-dimensional views (e.g. 1d, 2d, 3d, or even 4d). These views are arranged as if in a roadmap where each stop is a low dimensional view and the road between a smooth transition from one view to another -- the corresponding mathematical object is a graph with nodes (stops) and edges (roads) connecting them. This research is directed toward identifying interesting stops, roads, road trips, and entire roadmaps which, when explored, will reveal unanticipated structure in the set of digital data objects.