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4 September 2009Seventeen dubious methods to approximate the gradient for nonlinear filters with particle flow
We have investigated more than 17 distinct methods to approximate the gradient of the loghomotopy
for nonlinear filters. This is a challenging problem because the data are given as function
values at random points in high dimensional space. This general problem is important in
optimization, financial engineering, quantum chemistry, chemistry, physics and engineering. The
best general method that we have developed so far uses a simple idea borrowed from geology
combined with a fast approximate k-NN algorithm. Extensive numerical experiments for five
classes of problems shows that we get excellent performance.
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Fred Daum, Jim Huang, Misha Krichman, Talia Kohen, "Seventeen dubious methods to approximate the gradient for nonlinear filters with particle flow," Proc. SPIE 7445, Signal and Data Processing of Small Targets 2009, 74450V (4 September 2009); https://doi.org/10.1117/12.823519