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Minor changes to wording

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Markus Bullmann
2018-05-08 11:08:48 +02:00
parent 35e1f4e0b3
commit 9f358d69c9
5 changed files with 17 additions and 19 deletions
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tex/chapters/multivariate.tex
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@@ -24,9 +24,8 @@ The only exception is the Gaussian kernel, which is spherically symmetric and ha
In addition, only smoothing in the direction of the axes is possible.
If smoothing in other directions is necessary, the computation needs to be done on a prerotated sample set and the estimate needs to be rotated back to fit the original coordinate system \cite{wand1994fast}.
For the multivariate BKDE, in addition to the kernel function, the grid and the binning rules need to be extended to multivariate data.
Their extensions are rather straightforward, as the grid is easily defined on many dimensions.
Likewise, the ideas of common and linear binning rule scale with dimensionality \cite{wand1994fast}.
For the multivariate BKDE, in addition to the kernel function, the grid and the binning rules need to be extended to multivariate data, which is rather straightforward, as the grid is easily defined on many dimensions.
Likewise, the common and linear binning rule scale with dimensionality \cite{wand1994fast}.
In general, multi-dimensional filters are multi-dimensional convolution operations.
However, by utilizing the separability property of convolution, a straightforward and a more efficient implementation can be found.