28 lines
1.5 KiB
TeX
28 lines
1.5 KiB
TeX
\section{Experiments}
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We now empirically evaluate the accuracy of our method and compare its runtime performance with other state of the art approaches.
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To conclude our findings we present a real world example from a indoor localisation system.
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All tests are performed on a Intel Core \mbox{i5-7600K} CPU with a frequency of $4.5 \text{GHz}$, which supports the AVX2 instruction set, hence 256-bit wide SIMD registers are available.
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We compare our C++ implementation of the box filter based KDE to the KernSmooth R package and the \qq{FastKDE} implementation \cite{oBrien2016fast}.
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The KernSmooth packages provides a FFT-based BKDE implementation based on optimized C functions at its core.
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\subsection{Error}
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In order to quantity the accuracy of our method the mean integrated squared error (MISE) is used.
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The ground truth is given as a synthetic data set drawn from a mixture normal density.
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Clearly, the choice of the ground truth distribution affects the resulting error.
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However, as our method approximates the KDE it is only of interest to evaluate the closeness to the KDE and not to the ground truth itself.
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Therefore, the particular choice of the ground truth is only of minor importance here.
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At first we evaluate the accuracy of our method as a function of the bandwidth $h$ in comparison to the exact KDE and the BKDE.
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% kde, box filter, exbox in abhänigkeit von h (bild)
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% sample size und grid size text
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% fastKDE fehler vergleich macht kein sinn weil kernel und bandbreite unterschiedlich sind
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\subsection{Performance}
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\subsection{Real World}
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