Interactive Generative Manifold Learning Navy SBIR FY2012.2 Sol No.: Navy SBIR FY2012.2 Topic No.: N122-138 Topic Title: Interactive Generative Manifold Learning Proposal No.: N122-138-0505 Firm: Numerica Corporation 4850 Hahns Peak Drive Suite 200 Loveland, Colorado 80538 Contact: Randy Paffenroth Phone: (970) 612-2333 Web Site: www.numerica.us Abstract: Nonlinear manifold learning is an active area of mathematical research. Unfortunately, the extant literature has far less to offer on the problem of interactive nonlinear manifold learning. In other words, satisfactory nonlinear manifold learning approaches that put the ``human in the loop' are yet to be fully developed. Human steering of such calculations promises several advantages including, leveraging human expertise in sparse data environments, maximizing efficiency by allowing computational resources to be focused on areas of interest to the user, and augmenting the amount of useful information the user can glean from large and complicated data sets. Several questions immediately present themselves. What if the data is too voluminous to be processed all at once? What if one does not have all possible data at hand and must decide what additional data would be the most informative to synthesize, or to acquire? How does one best take advantage of the user's expertise and inject it into the problem? These considerations lead one inexorably to five core interactions between the user and the manifold learning algorithm that are not fully addressed in current manifold learning algorithms, namely: interpolation, extension, resampling, extrapolation, and visualization of the data by the user. Benefits: Algorithms for performing interactive non-linear dimension, such as those proposed herein, have wide applicability to many domains. Important examples include cyber security, mathematical finance, and web analytics where human-in-the-loop anomaly detection and uncertainty characterization are critical in analysis systems. There are many possible transition paths for machine learning within the Department of Defense, including cyber security and resiliency, hyper-spectral image (HSI) processing, data analytics for the intelligence community, and mine counter-measures for the Navy. Regarding the latter, the threat of underwater mines is dramatically rising in parallel with tensions around key, near-shore littoral zones and shallow-water chokepoints like the Suez Canal and Strait of Hormuz. In response, the Navy is replacing 30 FFG-7 Oliver Hazard Perry Class frigates, 14 MCM Avenger Class mine countermeasures vessels, and 12 MHC-51 Osprey Class coastal mine hunters, with approximately 55 Littoral Combat Ships. These ships have upgradeable mission modules with interchangeable components that enable the Navy to counter threats with enhanced capabilities as mission technologies evolve. This open architecture allows for more frequent refreshes of the state-of-the-art, such as the approach proposed in this Phase I. Return