\section{Cauchy\+Kernel Class Reference}
\label{classmlpack_1_1kernel_1_1CauchyKernel}\index{Cauchy\+Kernel@{Cauchy\+Kernel}}


The Cauchy kernel.  


\subsection*{Public Member Functions}
\begin{DoxyCompactItemize}
\item 
\textbf{ Cauchy\+Kernel} (double bandwidth=1.\+0)
\begin{DoxyCompactList}\small\item\em Construct the Cauchy kernel; by default, the bandwidth is 1.\+0. \end{DoxyCompactList}\item 
{\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\double \textbf{ Evaluate} (const Vec\+TypeA \&a, const Vec\+TypeB \&b)
\begin{DoxyCompactList}\small\item\em Evaluation of the Cauchy kernel. \end{DoxyCompactList}\item 
{\footnotesize template$<$typename Archive $>$ }\\void \textbf{ serialize} (Archive \&ar, const unsigned int)
\begin{DoxyCompactList}\small\item\em Serialize the kernel. \end{DoxyCompactList}\end{DoxyCompactItemize}


\subsection{Detailed Description}
The Cauchy kernel. 

Given two vector $ x $, $ y $, and a bandwidth $ \sigma $ (set in the constructor),

\[ K(x, y) = \frac{1}{1 + (\frac{|| x - y ||}{\sigma})^2}. \]

For more details, see the following published paper\+:


\begin{DoxyCode}
@inproceedings\{Basak2008,
  title=\{A least square kernel machine with box constraints\},
  author=\{Basak, Jayanta\},
  booktitle=\{Pattern Recognition, 2008. ICPR 2008. 19th International
      Conference on\},
  pages=\{1--4\},
  year=\{2008\},
  organization=\{IEEE\}
\}
\end{DoxyCode}
 

Definition at line 44 of file cauchy\+\_\+kernel.\+hpp.



\subsection{Constructor \& Destructor Documentation}
\mbox{\label{classmlpack_1_1kernel_1_1CauchyKernel_a928140be61e55757b48e7e02b1719400}} 
\index{mlpack\+::kernel\+::\+Cauchy\+Kernel@{mlpack\+::kernel\+::\+Cauchy\+Kernel}!Cauchy\+Kernel@{Cauchy\+Kernel}}
\index{Cauchy\+Kernel@{Cauchy\+Kernel}!mlpack\+::kernel\+::\+Cauchy\+Kernel@{mlpack\+::kernel\+::\+Cauchy\+Kernel}}
\subsubsection{Cauchy\+Kernel()}
{\footnotesize\ttfamily \textbf{ Cauchy\+Kernel} (\begin{DoxyParamCaption}\item[{double}]{bandwidth = {\ttfamily 1.0} }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}}



Construct the Cauchy kernel; by default, the bandwidth is 1.\+0. 



Definition at line 50 of file cauchy\+\_\+kernel.\+hpp.



\subsection{Member Function Documentation}
\mbox{\label{classmlpack_1_1kernel_1_1CauchyKernel_a7bc3cfc0ee3750ba84ee4dc7f62994ae}} 
\index{mlpack\+::kernel\+::\+Cauchy\+Kernel@{mlpack\+::kernel\+::\+Cauchy\+Kernel}!Evaluate@{Evaluate}}
\index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Cauchy\+Kernel@{mlpack\+::kernel\+::\+Cauchy\+Kernel}}
\subsubsection{Evaluate()}
{\footnotesize\ttfamily double Evaluate (\begin{DoxyParamCaption}\item[{const Vec\+TypeA \&}]{a,  }\item[{const Vec\+TypeB \&}]{b }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}}



Evaluation of the Cauchy kernel. 

This could be generalized to use any distance metric, not the Euclidean distance, but for now, the Euclidean distance is used.


\begin{DoxyTemplParams}{Template Parameters}
{\em Vec\+TypeA} & Type of first vector (arma\+::vec, arma\+::sp\+\_\+vec). \\
\hline
{\em Vec\+TypeB} & Type of second vector (arma\+::vec, arma\+::sp\+\_\+vec). \\
\hline
\end{DoxyTemplParams}

\begin{DoxyParams}{Parameters}
{\em a} & First vector. \\
\hline
{\em b} & Second vector. \\
\hline
\end{DoxyParams}
\begin{DoxyReturn}{Returns}
K(a, b). 
\end{DoxyReturn}


Definition at line 65 of file cauchy\+\_\+kernel.\+hpp.



References L\+Metric$<$ T\+Power, T\+Take\+Root $>$\+::\+Evaluate().

\mbox{\label{classmlpack_1_1kernel_1_1CauchyKernel_af0dd9205158ccf7bcfcd8ff81f79c927}} 
\index{mlpack\+::kernel\+::\+Cauchy\+Kernel@{mlpack\+::kernel\+::\+Cauchy\+Kernel}!serialize@{serialize}}
\index{serialize@{serialize}!mlpack\+::kernel\+::\+Cauchy\+Kernel@{mlpack\+::kernel\+::\+Cauchy\+Kernel}}
\subsubsection{serialize()}
{\footnotesize\ttfamily void serialize (\begin{DoxyParamCaption}\item[{Archive \&}]{ar,  }\item[{const unsigned}]{int }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}}



Serialize the kernel. 



Definition at line 75 of file cauchy\+\_\+kernel.\+hpp.



The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize}
\item 
/var/www/mlpack.\+ratml.\+org/mlpack.\+org/\+\_\+src/mlpack-\/3.\+3.\+2/src/mlpack/core/kernels/\textbf{ cauchy\+\_\+kernel.\+hpp}\end{DoxyCompactItemize}