Information Is In the Maps: Representations & Algorithms for Mapping among Geometric Data.

摘要

The project has developed tools for understanding informative, structure-preserving and composition-revealing maps between multiple geometric data sets in 2D, 3D, and higher dimensions. The discovery of such informative maps is deeply interesting, because our comprehension of a geometric data set is often based on understanding the relationships among its parts, or its connections to other data sets that may share the same or similar structure. Towards this end, we have studied a variety of neighborhood descriptors in geometric data sets and their properties. Such descriptors help establish useful correspondences and seed the process of finding good maps. We have also investigated networks of maps and the consistency of information transport in such networks. The space of all maps is a huge space and an important part of the project has addressed the problem of finding compact representations and encodings for the much smaller spaces of interesting maps within a specific application. The machinery developed here has proven of use across a broad spectrum of disciplines that use geometric data, has helped generate novel mathematics and algorithms, and has made connections with cognitive science concepts and ideas.