Statistical and computational methodology for visualizing high-dimensional digital data

加拿大人可以访问大量的数字数据对象，其形式包括文档、网站、图像、声音和视频。这些形式中的任何一种的一组实例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。拟议的研究旨在开发统计方法和软件，使人们能够通过以一系列低维视图(例如，一维、二维、三维或甚至四维)的可视方式来有意义地探索任何此类集合。这些视图就像是在路线图中排列的，其中每个停靠点都是低维视图，从一个视图到另一个视图之间的道路平滑过渡--相应的数学对象是具有连接它们的节点(停靠点)和边(道路)的图形。这项研究旨在识别有趣的停靠、道路、公路旅行和整个路线图，当进行探索时，将揭示数字数据对象集中的意外结构。

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.