Statistical and computational methodology for visualizing high-dimensional digital data

加拿大人可以接触到大量的数字数据对象，包括文件、网站、图像、声音和视频。这些形式中的任何一种的一组实例都可以表示为高维空间（可能是10或100或1000维）中的一组数据点；这些点在空间中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，这将允许人们通过将其可视化地呈现为一系列低维视图（例如1d， 2d, 3d，甚至4d）来有意义地探索任何此类集合。这些视图就像在路线图中一样排列，其中每个站点都是一个低维视图，而从一个视图平滑过渡到另一个视图之间的道路——相应的数学对象是一个图，其中有节点（站点）和边缘（道路）连接它们。这项研究旨在识别有趣的站点、道路、公路旅行和整个路线图，当探索时，将揭示数字数据对象集合中意想不到的结构。

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.