Program Manager: Mark A. Neifeld, Ph.D
 The Topological Data Analysis (TDA) Program aims to develop the mathematical concepts and techniques necessary to determine the fundamental geometric structures underlying massive data sets and then develop further tools to exploit that knowledge.
The TDA Program is developing new mathematical methods and techniques to study massive data sets that arise in a variety of military situations. These massive databases and high-volume data flows represented in digital form have hidden, highly nonlinear, geometric structures and properties. In particular, many important questions in data analysis are qualitative in nature whereas current statistical methods suffer from the “curse of dimensionality;” that is, they become both harder to compute and less informative as their inputs increase to enormous sizes. As current statistical methods are ill-suited to detect such qualitative structures, the project recognizes that it is essential to understand these properties before attempting to perform more precise quantitative analysis; for example, it is better to distinguish shapes by understanding them qualitatively rather than resorting to database comparisons. In turn, this understanding will help develop tools to exploit this qualitative structure to extract important practical information.
The fundamental mathematical, computational, and statistical tools developed in this program will have broad impact across several avenues of defense application as the data sets amenable to the proposed analysis reside throughout the military. Examples include sensor, intelligence, biological, logistical, and other DoD-critical applications.
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