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toni
2018-02-06 10:51:54 +01:00
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commit 00754a00da
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tex/bare_conf.tex
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%% bare_conf.tex
%% V1.4b
%% 2015/08/26
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8b or later) with an IEEE
%% conference paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/pkg/ieeetran
%% and
%% http://www.ieee.org/
%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE!
%% User assumes all risk.
%% In no event shall the IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including **
%% ** renaming them and changing author support contact information. **
%%*************************************************************************
% *** Authors should verify (and, if needed, correct) their LaTeX system ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. The IEEE's font choices and paper sizes can ***
% *** trigger bugs that do not appear when using other class files. *** ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/
\documentclass[conference]{IEEEtran}
% Some Computer Society conferences also require the compsoc mode option,
% but others use the standard conference format.
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
%\documentclass[conference]{../sty/IEEEtran}
% needed packages
\usepackage{color, colortbl}
%\usepackage[table]{xcolor}
\usepackage{cite}
% \usepackage[pdftex]{graphicx}
% \graphicspath{{../pdf/}{../jpeg/}}
% \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\usepackage{amsmath}
%\usepackage{array}
% \usepackage[caption=false,font=footnotesize]{subfig}
%\usepackage{url}
\usepackage{graphicx}
\usepackage{amsfonts}
% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}
\usepackage[cmex10]{amsmath}
\interdisplaylinepenalty=2500
\usepackage{array}
\usepackage{mdwmath}
\usepackage{mdwtab}
\usepackage{eqparbox}
\usepackage{epstopdf}
%\usepackage{ulem}
\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{subcaption}
% replacement for the SI package
\newcommand{\SI}[2]{\ensuremath{#1}\text{\,#2}}
\newcommand{\SIrange}[3]{\ensuremath{#1} to \ensuremath{#2}\text{\,#3}}
% units for the SI package
\newcommand{\centimeter}{cm}
\newcommand{\meter}{m}
\newcommand{\per}{/}
\newcommand{\milli}{m}
\newcommand{\second}{s}
\newcommand{\giga}{G}
\newcommand{\hertz}{Hz}
\newcommand{\dBm}{dBm}
\newcommand{\percent}{\%}
\newcommand{\decibel}{dB}
\newcommand{\dB}{dB}
\newcommand{\hpa}{hPa}
\newcommand{\degree}{\ensuremath{^{\circ}}}
\newcommand{\dop} [1]{\ensuremath{ \mathop{\mathrm{d}#1} }}
\newcommand{\R} {\ensuremath{ \mathbf{R} }}
@@ -22,6 +109,66 @@
\newcommand{\qq} [1]{``#1''}
% missing math operators
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}
% vector and matrix typesetting
\renewcommand{\vec}[1]{\boldsymbol{#1}} % italic and greek symbols
\newcommand{\mat}[1]{\vec{#1}} % the same as vec
%other macros
\newcommand{\noStep}{\overline{\text{step}}}
% gfx include folder
\graphicspath{ {gfx/} {gfx/eval}}
% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}
% input stuff
\input{misc/keywords}
\input{misc/functions}
% the title of the IPIN conference
%\markboth{2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 18-21 September 2017, Sapporo, Japan}{2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 18-21 September 2017, Sapporo, Japan}
%\IEEEoverridecommandlockouts
%\IEEEpubid{\makebox[\columnwidth]{\hfill XXX-X-XXXX-XXXX-X/XX/\$XX.XX~\copyright~2018 IEEE}
%\hspace{\columnsep}\makebox[\columnwidth]{ }}
\makeatletter
\let\old@ps@headings\ps@headings
\let\old@ps@IEEEtitlepagestyle\ps@IEEEtitlepagestyle
\def\confheader#1{%
% for all pages except the first
\def\ps@headings{%
\old@ps@headings%
\def\@oddhead{\strut\hfill#1\hfill\strut}%
\def\@evenhead{\strut\hfill#1\hfill\strut}%
}%
% for the first page
\def\ps@IEEEtitlepagestyle{%
\old@ps@IEEEtitlepagestyle%
\def\@oddhead{\strut\hfill#1\hfill\strut}%
\def\@evenhead{\strut\hfill#1\hfill\strut}%
}%
\ps@headings%
}
\makeatother
%\confheader{2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 18-21 September 2017, Sapporo, Japan}
% ensure each page shows the headings
%\pagestyle{headings}
\begin{document}
%
% paper title
@@ -30,32 +177,46 @@
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls\\ for IEEE Conferences}
\title{Fast Kernel Density Estimation using blah und blub}
% author names and affiliations
% use a multiple column layout for up to three different
% affiliations
\author{
\IEEEauthorblockN{Markus Bullmann, Toni Fetzer, Frank Ebner, and Frank Deinzer}%
\IEEEauthorblockA{%
Faculty of Computer Science and Business Information Systems\\
University of Applied Sciences W\"urzburg-Schweinfurt\\
W\"urzburg, Germany\\
\{markus.bullmann, toni.fetzer, frank.ebner, frank.deinzer\}@fhws.de\\
}
\IEEEauthorblockN{Markus Bullmann, Toni Fetzer, Frank Ebner, and Frank Deinzer}%
\IEEEauthorblockA{%
Faculty of Computer Science and Business Information Systems\\
University of Applied Sciences W\"urzburg-Schweinfurt\\
W\"urzburg, Germany\\
\{markus.bullmann, toni.fetzer, frank.ebner, frank.deinzer\}@fhws.de\\
}
\and
\IEEEauthorblockN{Marcin Grzegorzek}
\IEEEauthorblockA{%
Pattern Recognition Group \\
University of Siegen\\
Siegen, Germany\\
marcin.grzegorzek@uni-siegen.de
}%
}
% conference papers do not typically use \thanks and this command
% is locked out in conference mode. If really needed, such as for
% the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
% after \documentclass
% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}
% make the title area
\maketitle
\begin{abstract}
The abstract goes here.
\end{abstract}
% no keywords
% As a general rule, do not put math, special symbols or citations
% in the abstract
\input{chapters/abstract}
% For peer review papers, you can put extra information on the cover
@@ -69,105 +230,38 @@ The abstract goes here.
\IEEEpeerreviewmaketitle
\input{chapters/introduction}
\section{Introduction}
% KDE wellknown nonparametic estimation method
% Flexibility is paid with slow speed
% Finding optimal bandwidth
% Expensive computation
\input{chapters/relatedwork}
\section{Related work}
% original work rosenblatt/parzen
% binned version silverman, scott, härdle
% -> Fourier transfom
% other approaches Fast Gaussian Transform
\input{chapters/kde}
\section{Kernel Density Estimation}
% KDE by rosenblatt and parzen
% general KDE
% Gauss Kernel
% Formula Gauss KDE
% -> complexity/operation count
% Binned KDE
% Binned Gauss KDE
% -> complexity/operation count
The histogram is a simple and for a long time the most used non-parametric estimator.
However, its inability to produce a continuous estimate dismisses it for many applications where a smooth distribution is assumed.
In contrast, the KDE is often the preferred tool because of its ability to produce a continuous estimate and its flexibility.
Given $n$ independently observed realizations of the observation set $X=(x_1,\dots,x_n)$, the kernel density estimate $\hat{f}_n$ of the density function $f$ of the underlying distribution is given with
\begin{equation}
\label{eq:kde}
\hat{f}_n = \frac{1}{nh} \sum_{i=1}^{n} K \left( \frac{x-X_i}{h} \right) \text{,} %= \frac{1}{n} \sum_{i=1}^{n} K_h(x-x_i)
\end{equation}
where $K$ is the kernel function and $h\in\R^+$ is an arbitrary smoothing parameter called bandwidth.
While any density function can be used as the kernel function $K$ (such that $\int K(u) \dop{u} = 1$), a variety of popular choices of the kernel function $K$ exits.
In practice the Gaussian kernel is commonly used:
\begin{equation}
K(u)=\frac{1}{\sqrt{2\pi}} \expp{- \frac{u^2}{2} }
\end{equation}
\begin{equation}
\hat{f}_n = \frac{1}{nh\sqrt{2\pi}} \sum_{i=1}^{n} \expp{-\frac{(x-X_i)^2}{2h^2}}
\end{equation}
\section{Moving Average Filter}
% Basic box filter formula
% Recursive form
% Gauss Blur Filter
% Repetitive Box filter to approx Gauss
% Simple multipass, n/m approach, extended box filter
The moving average filter is a simplistic filter which takes an input function $x$ and produces a second function $y$.
A single output value is computed by taking the average of a number of values symmetrical around a single point in the input.
The number of values in the average can also be seen as the width $w=2r+1$, where $r$ is the \qq{radius} of the filter.
The computation of an output value using a moving average filter of radius $r$ is defined as
\begin{equation}
\label{eq:symMovAvg}
y[i]=\frac{1}{2r+1} \sum_{j=-r}^{r}x[i+j] \text{.}
\end{equation}
It is well-known that a moving average filter can approximate a Gaussian filter by repetitive recursive computations.
As is known the Gaussian filter is parametrized by its standard deviation $\sigma$.
To approximate a Gaussian filter one needs to express a given $\sigma$ in terms of moving average filters.
\section{Combination}
\section{Experiments}
\section{Conclusion}
The conclusion goes here.
\input{chapters/mvg}
\input{chapters/usage}
\input{chapters/experiments}
\input{chapters/conclusion}
% conference papers do not normally have an appendix
% use section* for acknowledgment
%\section*{Acknowledgment}
%The authors would like to thank...
% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
% balancing
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}
% references section
\bibliographystyle{IEEEtran}
\bibliography{IEEEabrv,egbib}
\end{document}