Statistical and computational methodology for visualizing high-dimensional digital data

加拿大人可以访问文档、网站、图像、声音和视频等形式的大量数字数据对象。 这些形式中的任何一个的一组实例都可以表示为高维空间（可能是10维、100维或1000维）中的一组数据点;这些点在空间中的相对位置的结构与原始对象之间的概念关系相匹配。 拟议的研究是针对统计方法和软件的发展，这将使人们能够有意义地探索任何这样的集合，通过将其视觉上呈现为一系列低维视图（例如1D，2D，3D，甚至4D）。 这些视图被安排得好像在一个路线图中，其中每个站点是一个低维视图，而从一个视图到另一个视图之间的道路是一个平滑的过渡-相应的数学对象是一个具有节点（站点）和连接它们的边（道路）的图。 这项研究是针对确定有趣的停止，道路，公路旅行，和整个路线图，当探索，将揭示意想不到的结构，在一组数字数据对象。

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.