314 research outputs found
Nonlinear model order reduction via Dynamic Mode Decomposition
We propose a new technique for obtaining reduced order models for nonlinear
dynamical systems. Specifically, we advocate the use of the recently developed
Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the
nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix
that correlates spatial features while simultaneously associating the activity
with periodic temporal behavior. With this decomposition, one can obtain a
fully reduced dimensional surrogate model and avoid the evaluation of the
nonlinear term in the online stage. This allows for an impressive speed up of
the computational cost, and, at the same time, accurate approximations of the
problem. We present a suite of numerical tests to illustrate our approach and
to show the effectiveness of the method in comparison to existing approaches
Selecting a Small Set of Optimal Gestures from an Extensive Lexicon
Finding the best set of gestures to use for a given computer recognition
problem is an essential part of optimizing the recognition performance while
being mindful to those who may articulate the gestures. An objective function,
called the ellipsoidal distance ratio metric (EDRM), for determining the best
gestures from a larger lexicon library is presented, along with a numerical
method for incorporating subjective preferences. In particular, we demonstrate
an efficient algorithm that chooses the best gestures from a lexicon of
gestures where typically using a weighting of both subjective and
objective measures.Comment: 27 pages, 7 figure
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