Noncommutative Adaptive Estimation for Dimension Reduction and Data Clustering
Abstract
The purpose of this research is to develop and justify algorithms to resolve several important tasks in processing large, complicated data sets, such as dimension reduction and data clustering. In particular, we propose to fully automate several geometric techniques for dimension reduction which currently involve hand-picking a discrete approximation to a geometric operator on a manifold, such as the Laplace- Beltrami operator or the heat operator. The eigenvalues and eigenvectors of these operators may then be used for data clustering and dimension reduction. Mathematically, our research involves developing non-commutative analogues of fundamental non-asymptotic statistical techniques, which we anticipate will have other important applications in the future. This research falls directly in the purview of the Office of Naval Research Integrated Research Portfolio of Information, Cyber, and Spectrum Superiority, as described in the Naval Research Enterprise Addendum to the Naval Research and Development Framework [28], and in particular addresses the Command and Control and Decision-Making Superiority aspects of the portfolio. We anticipate that the research will result in between 3-4 journal articles, at least 4 conference presentations, and a software package containing the algorithms developed.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 30, 2019
- Source ID
- N629091912134
Entities
People
- Antonio Rieser
Organizations
- CIMAT Center for Mathematical Research
- Office of Naval Research
- United States Navy