Some text

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}
+\author{	
-\IEEEauthorblockA{School of Electrical and\\Computer Engineering\\
+    
-Georgia Institute of Technology\\
+    \IEEEauthorblockN{Markus Bullmann, Toni Fetzer, Frank Ebner, and Frank Deinzer}%
-Atlanta, Georgia 30332--0250\\
+    \IEEEauthorblockA{%
-Email: http://www.michaelshell.org/contact.html}
+        Faculty of Computer Science and Business Information Systems\\ 
-\and
+        University of Applied Sciences W\"urzburg-Schweinfurt\\
-\IEEEauthorblockN{Homer Simpson}
+        W\"urzburg, Germany\\
-\IEEEauthorblockA{Twentieth Century Fox\\
+        \{markus.bullmann, toni.fetzer, frank.ebner, frank.deinzer\}@fhws.de\\		
-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}}
 
 
 \maketitle
@@ -70,29 +68,49 @@ The abstract goes here.
 
 
 \section{Introduction}
-% no \IEEEPARstart
+% KDE wellknown nonparametic estimation method
-This demo file is intended to serve as a ``starter file''
+% Flexibility is paid with slow speed
-for IEEE conference papers produced under \LaTeX\ using
+% Finding optimal bandwidth
-IEEEtran.cls version 1.8b and later.
+% Expensive computation
-% 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.
 
 \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}