\section{Gaussian\+Kernel Class Reference} \label{classmlpack_1_1kernel_1_1GaussianKernel}\index{Gaussian\+Kernel@{Gaussian\+Kernel}} The standard Gaussian kernel. \subsection*{Public Member Functions} \begin{DoxyCompactItemize} \item \textbf{ Gaussian\+Kernel} () \begin{DoxyCompactList}\small\item\em Default constructor; sets bandwidth to 1.\+0. \end{DoxyCompactList}\item \textbf{ Gaussian\+Kernel} (const double bandwidth) \begin{DoxyCompactList}\small\item\em Construct the Gaussian kernel with a custom bandwidth. \end{DoxyCompactList}\item double \textbf{ Bandwidth} () const \begin{DoxyCompactList}\small\item\em Get the bandwidth. \end{DoxyCompactList}\item void \textbf{ Bandwidth} (const double bandwidth) \begin{DoxyCompactList}\small\item\em Modify the bandwidth. \end{DoxyCompactList}\item {\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\double \textbf{ Convolution\+Integral} (const Vec\+TypeA \&a, const Vec\+TypeB \&b) \begin{DoxyCompactList}\small\item\em Obtain a convolution integral of the Gaussian kernel. \end{DoxyCompactList}\item {\footnotesize template$<$typename Vec\+TypeA , typename Vec\+TypeB $>$ }\\double \textbf{ Evaluate} (const Vec\+TypeA \&a, const Vec\+TypeB \&b) const \begin{DoxyCompactList}\small\item\em Evaluation of the Gaussian kernel. \end{DoxyCompactList}\item double \textbf{ Evaluate} (const double t) const \begin{DoxyCompactList}\small\item\em Evaluation of the Gaussian kernel given the distance between two points. \end{DoxyCompactList}\item double \textbf{ Gamma} () const \begin{DoxyCompactList}\small\item\em Get the precalculated constant. \end{DoxyCompactList}\item double \textbf{ Gradient} (const double t) const \begin{DoxyCompactList}\small\item\em Evaluation of the gradient of Gaussian kernel given the distance between two points. \end{DoxyCompactList}\item double \textbf{ Gradient\+For\+Squared\+Distance} (const double t) const \begin{DoxyCompactList}\small\item\em Evaluation of the gradient of Gaussian kernel given the squared distance between two points. \end{DoxyCompactList}\item double \textbf{ Normalizer} (const size\+\_\+t dimension) \begin{DoxyCompactList}\small\item\em Obtain the normalization constant of the Gaussian 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 standard Gaussian kernel. Given two vectors $ x $, $ y $, and a bandwidth $ \mu $ (set in the constructor), \[ K(x, y) = \exp(-\frac{|| x - y ||^2}{2 \mu^2}). \] The implementation is all in the header file because it is so simple. Definition at line 34 of file gaussian\+\_\+kernel.\+hpp. \subsection{Constructor \& Destructor Documentation} \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a3e3737b271f9d6a43319dd5aedc8390e}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Gaussian\+Kernel@{Gaussian\+Kernel}} \index{Gaussian\+Kernel@{Gaussian\+Kernel}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Gaussian\+Kernel()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily \textbf{ Gaussian\+Kernel} (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Default constructor; sets bandwidth to 1.\+0. Definition at line 40 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a863246483e645a55547661d9d470667e}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Gaussian\+Kernel@{Gaussian\+Kernel}} \index{Gaussian\+Kernel@{Gaussian\+Kernel}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Gaussian\+Kernel()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily \textbf{ Gaussian\+Kernel} (\begin{DoxyParamCaption}\item[{const double}]{bandwidth }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Construct the Gaussian kernel with a custom bandwidth. \begin{DoxyParams}{Parameters} {\em bandwidth} & The bandwidth of the kernel ( $\mu$). \\ \hline \end{DoxyParams} Definition at line 48 of file gaussian\+\_\+kernel.\+hpp. \subsection{Member Function Documentation} \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_ae9cbd816179d6c36036139ccc8fea8c8}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Bandwidth@{Bandwidth}} \index{Bandwidth@{Bandwidth}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Bandwidth()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Bandwidth (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the bandwidth. Definition at line 135 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a73bfbbc3f9a234670309c4895a7321e1}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Bandwidth@{Bandwidth}} \index{Bandwidth@{Bandwidth}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Bandwidth()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily void Bandwidth (\begin{DoxyParamCaption}\item[{const double}]{bandwidth }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Modify the bandwidth. This takes an argument because we must update the precalculated constant (gamma). Definition at line 139 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_af3077f924263d1932950f4f7176c93eb}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Convolution\+Integral@{Convolution\+Integral}} \index{Convolution\+Integral@{Convolution\+Integral}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Convolution\+Integral()} {\footnotesize\ttfamily double Convolution\+Integral (\begin{DoxyParamCaption}\item[{const Vec\+TypeA \&}]{a, }\item[{const Vec\+TypeB \&}]{b }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Obtain a convolution integral of the Gaussian kernel. \begin{DoxyParams}{Parameters} {\em a} & First vector. \\ \hline {\em b} & Second vector. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} The convolution integral. \end{DoxyReturn} Definition at line 127 of file gaussian\+\_\+kernel.\+hpp. References Gaussian\+Kernel\+::\+Evaluate(), L\+Metric$<$ T\+Power, T\+Take\+Root $>$\+::\+Evaluate(), and Gaussian\+Kernel\+::\+Normalizer(). \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a84c3aeba25ea7703bd2d4f85a54301da}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Evaluate()\hspace{0.1cm}{\footnotesize\ttfamily [1/2]}} {\footnotesize\ttfamily double Evaluate (\begin{DoxyParamCaption}\item[{const Vec\+TypeA \&}]{a, }\item[{const Vec\+TypeB \&}]{b }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the Gaussian 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\+Type} & Type of vector (likely arma\+::vec or arma\+::spvec). \\ \hline \end{DoxyTemplParams} \begin{DoxyParams}{Parameters} {\em a} & First vector. \\ \hline {\em b} & Second vector. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(a, b) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 65 of file gaussian\+\_\+kernel.\+hpp. References L\+Metric$<$ T\+Power, T\+Take\+Root $>$\+::\+Evaluate(). Referenced by Gaussian\+Kernel\+::\+Convolution\+Integral(). \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a031ed73efe13c6e6bc805006bd249238}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Evaluate@{Evaluate}} \index{Evaluate@{Evaluate}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Evaluate()\hspace{0.1cm}{\footnotesize\ttfamily [2/2]}} {\footnotesize\ttfamily double Evaluate (\begin{DoxyParamCaption}\item[{const double}]{t }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the Gaussian kernel given the distance between two points. \begin{DoxyParams}{Parameters} {\em t} & The distance between the two points the kernel is evaluated on. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(t) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 78 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_aebe61d5199ae22a5d9101a5cee3dfbd7}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Gamma@{Gamma}} \index{Gamma@{Gamma}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Gamma()} {\footnotesize\ttfamily double Gamma (\begin{DoxyParamCaption}{ }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Get the precalculated constant. Definition at line 146 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a6abdb9c6ceb3252af988ab5fb5f13764}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Gradient@{Gradient}} \index{Gradient@{Gradient}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Gradient()} {\footnotesize\ttfamily double Gradient (\begin{DoxyParamCaption}\item[{const double}]{t }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the gradient of Gaussian kernel given the distance between two points. \begin{DoxyParams}{Parameters} {\em t} & The distance between the two points the kernel is evaluated on. \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(t) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 92 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_a7f2c3729f3cac0b0b327ec28ccb8e1d3}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Gradient\+For\+Squared\+Distance@{Gradient\+For\+Squared\+Distance}} \index{Gradient\+For\+Squared\+Distance@{Gradient\+For\+Squared\+Distance}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Gradient\+For\+Squared\+Distance()} {\footnotesize\ttfamily double Gradient\+For\+Squared\+Distance (\begin{DoxyParamCaption}\item[{const double}]{t }\end{DoxyParamCaption}) const\hspace{0.3cm}{\ttfamily [inline]}} Evaluation of the gradient of Gaussian kernel given the squared distance between two points. \begin{DoxyParams}{Parameters} {\em t} & The squared distance between the two points \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} K(t) using the bandwidth ( $\mu$) specified in the constructor. \end{DoxyReturn} Definition at line 104 of file gaussian\+\_\+kernel.\+hpp. \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_aa500736f2a5dac08fa9027543c2b05cb}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!Normalizer@{Normalizer}} \index{Normalizer@{Normalizer}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}} \subsubsection{Normalizer()} {\footnotesize\ttfamily double Normalizer (\begin{DoxyParamCaption}\item[{const size\+\_\+t}]{dimension }\end{DoxyParamCaption})\hspace{0.3cm}{\ttfamily [inline]}} Obtain the normalization constant of the Gaussian kernel. \begin{DoxyParams}{Parameters} {\em dimension} & \\ \hline \end{DoxyParams} \begin{DoxyReturn}{Returns} the normalization constant \end{DoxyReturn} Definition at line 114 of file gaussian\+\_\+kernel.\+hpp. References M\+\_\+\+PI. Referenced by Gaussian\+Kernel\+::\+Convolution\+Integral(). \mbox{\label{classmlpack_1_1kernel_1_1GaussianKernel_af0dd9205158ccf7bcfcd8ff81f79c927}} \index{mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+Kernel}!serialize@{serialize}} \index{serialize@{serialize}!mlpack\+::kernel\+::\+Gaussian\+Kernel@{mlpack\+::kernel\+::\+Gaussian\+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 150 of file gaussian\+\_\+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.\+1/src/mlpack/core/kernels/\textbf{ gaussian\+\_\+kernel.\+hpp}\end{DoxyCompactItemize}