FHWS/Fusion2018
Archived
4
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Intro & related work

Browse Source
This commit is contained in:
Markus Bullmann
2018-02-13 17:30:32 +01:00
parent 4aa3ff5e30
commit 7b82b8247c
4 changed files with 122 additions and 6 deletions
Download Patch File Download Diff File Expand all files Collapse all files

15
tex/chapters/introduction.tex
View File

@@ -28,14 +28,19 @@ We formalize this ...
Our experiments support our ..
}
In this paper, a novel approximation approach for rapid computation of the KDE is presented.
%Therefore, this paper presents a novel approximation approach for rapid computation of the KDE.
%In this paper, a well known approximation of the Gaussian filter is used to speed up the computation of the KDE.
In this paper, a novel approximation approach for rapid computation of the KDE is presented.
The basic idea is to interpret the estimation problem as a filtering operation.
We show that computing the KDE with a Gaussian kernel on pre-binned data is equal to applying a Gaussian filter on the binned data.
This allows us to use a well known approximation scheme for Gaussian filters using the box filter.
Multiple recursion of a box filter yields an approximative Gaussian filter \cite{kovesi2010fast}.
This process converges quite fast to a reasonable close approximation of the ideal Gaussian.
In addition, a box filter can be computed extremely fast by a computer, due to its intrinsic simplicity.
While the idea to use several box filter passes to approximate a Gaussian has been around for a long, the application to obtain a fast KDE is new.
% time sequential, fixed computation time, pre binned data!!
% KDE wellknown nonparametic estimation method
% Flexibility is paid with slow speed