diff --git a/tex/bare_conf.tex b/tex/bare_conf.tex index e2c6c28..eea1d72 100644 --- a/tex/bare_conf.tex +++ b/tex/bare_conf.tex @@ -15,6 +15,10 @@ % correct bad hyphenation here \hyphenation{op-tical net-works semi-conduc-tor} + +\newcommand{\dop} [1]{\ensuremath{ \mathop{\mathrm{d}#1} }} +\newcommand{\R} {\ensuremath{ \mathbf{R} }} + \begin{document} % % paper title @@ -29,22 +33,16 @@ % author names and affiliations % use a multiple column layout for up to three different % affiliations -\author{\IEEEauthorblockN{Michael Shell} -\IEEEauthorblockA{School of Electrical and\\Computer Engineering\\ -Georgia Institute of Technology\\ -Atlanta, Georgia 30332--0250\\ -Email: http://www.michaelshell.org/contact.html} -\and -\IEEEauthorblockN{Homer Simpson} -\IEEEauthorblockA{Twentieth Century Fox\\ -Springfield, USA\\ -Email: homer@thesimpsons.com} -\and -\IEEEauthorblockN{James Kirk\\ and Montgomery Scott} -\IEEEauthorblockA{Starfleet Academy\\ -San Francisco, California 96678--2391\\ -Telephone: (800) 555--1212\\ -Fax: (888) 555--1212}} +\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\\ + } +} \maketitle @@ -70,29 +68,49 @@ The abstract goes here. \section{Introduction} -% no \IEEEPARstart -This demo file is intended to serve as a ``starter file'' -for IEEE conference papers produced under \LaTeX\ using -IEEEtran.cls version 1.8b and later. -% You must have at least 2 lines in the paragraph with the drop letter -% (should never be an issue) -I wish you the best of success. - -\hfill mds - -\hfill August 26, 2015 - -\subsection{Subsection Heading Here} -Subsection text here. - - -\subsubsection{Subsubsection Heading Here} -Subsubsection text here. +% KDE wellknown nonparametic estimation method +% Flexibility is paid with slow speed +% Finding optimal bandwidth +% Expensive computation \section{Related work} +% original work rosenblatt/parzen +% binned version silverman, scott, härdle +% -> Fourier transfom +% other approaches Fast Gaussian Transform + +\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:kede} +\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. +Commonly the Gaussian kernel is used. + + +\section{Box Filter} +% Basic box filter formula +% Recursive form +% Gauss Blur Filter +% Repetitive Box filter to approx Gauss +% Simple multipass, n/m approach, extended box filter + +\section{Combination} -\section{Bla} -\section{Blub} \section{Experiments}