Classification of Data Bundles via Parameter Spaces.

摘要

Over the course of this project we developed a mathematical representation of data, which we refer to as data bundles. This approach provides a mechanism for encoding the data including aspects of the signal that might normally be removed to simplify data processing. Motivated by the mathematics of fiber bundles, a data bundle provides a flexible representation of information that embraces variations that one would normally attempt to limit, or exclude entirely. Such an approach motivates the idea of intelligent data acquisition wherein the state of an object may actually be varied to enrich the data collection process. The data bundle is a natural way to encode information which can then be viewed as a point on a variety of parameter spaces such as Grassmann manifolds, Flag manifolds, or Stiefel manifolds. Each setting provides a different view of the data and similarity measures may be constructed in these settings to optimize discriminatory strength of any classification system. The development of the basic mathematical theory of data bundles into practical algorithms will bring fundamentally new tools to bear on the problem of processing large quantities of streaming data.