\section{mlpack\+:\+:kernel Namespace Reference}
\label{namespacemlpack_1_1kernel}\index{mlpack\+::kernel@{mlpack\+::kernel}}


Kernel functions.  


\subsection*{Classes}
\begin{DoxyCompactItemize}
\item 
class \textbf{ Cauchy\+Kernel}
\begin{DoxyCompactList}\small\item\em The Cauchy kernel. \end{DoxyCompactList}\item 
class \textbf{ Cosine\+Distance}
\begin{DoxyCompactList}\small\item\em The cosine distance (or cosine similarity). \end{DoxyCompactList}\item 
class \textbf{ Epanechnikov\+Kernel}
\begin{DoxyCompactList}\small\item\em The Epanechnikov kernel, defined as. \end{DoxyCompactList}\item 
class \textbf{ Example\+Kernel}
\begin{DoxyCompactList}\small\item\em An example kernel function. \end{DoxyCompactList}\item 
class \textbf{ Gaussian\+Kernel}
\begin{DoxyCompactList}\small\item\em The standard Gaussian kernel. \end{DoxyCompactList}\item 
class \textbf{ Hyperbolic\+Tangent\+Kernel}
\begin{DoxyCompactList}\small\item\em Hyperbolic tangent kernel. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits}
\begin{DoxyCompactList}\small\item\em This is a template class that can provide information about various kernels. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Cauchy\+Kernel $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits for the Cauchy kernel. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Cosine\+Distance $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits for the cosine distance. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Epanechnikov\+Kernel $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits for the Epanechnikov kernel. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Gaussian\+Kernel $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits for the Gaussian kernel. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Laplacian\+Kernel $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits of the Laplacian kernel. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Spherical\+Kernel $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits for the spherical kernel. \end{DoxyCompactList}\item 
class \textbf{ Kernel\+Traits$<$ Triangular\+Kernel $>$}
\begin{DoxyCompactList}\small\item\em Kernel traits for the triangular kernel. \end{DoxyCompactList}\item 
class \textbf{ K\+Means\+Selection}
\begin{DoxyCompactList}\small\item\em Implementation of the kmeans sampling scheme. \end{DoxyCompactList}\item 
class \textbf{ Laplacian\+Kernel}
\begin{DoxyCompactList}\small\item\em The standard Laplacian kernel. \end{DoxyCompactList}\item 
class \textbf{ Linear\+Kernel}
\begin{DoxyCompactList}\small\item\em The simple linear kernel (dot product). \end{DoxyCompactList}\item 
class \textbf{ Nystroem\+Method}
\item 
class \textbf{ Ordered\+Selection}
\item 
class \textbf{ Polynomial\+Kernel}
\begin{DoxyCompactList}\small\item\em The simple polynomial kernel. \end{DoxyCompactList}\item 
class \textbf{ P\+Spectrum\+String\+Kernel}
\begin{DoxyCompactList}\small\item\em The p-\/spectrum string kernel. \end{DoxyCompactList}\item 
class \textbf{ Random\+Selection}
\item 
class \textbf{ Spherical\+Kernel}
\begin{DoxyCompactList}\small\item\em The spherical kernel, which is 1 when the distance between the two argument points is less than or equal to the bandwidth, or 0 otherwise. \end{DoxyCompactList}\item 
class \textbf{ Triangular\+Kernel}
\begin{DoxyCompactList}\small\item\em The trivially simple triangular kernel, defined by. \end{DoxyCompactList}\end{DoxyCompactItemize}


\subsection{Detailed Description}
Kernel functions. 

This namespace contains kernel functions, which evaluate some kernel function $ K(x, y) $ for some arbitrary vectors $ x $ and $ y $ of the same dimension. The single restriction on the function $ K(x, y) $ is that it must satisfy Mercer\textquotesingle{}s condition\+:

\[ \int \int K(x, y) g(x) g(y) dx dy \ge 0 \]

for all square integrable functions $ g(x) $.

The kernels in this namespace all implement the Kernel\+Type policy. For more information, see \doxyref{The Kernel\+Type policy documentation}{p.}{kernels}.