.TH "mlpack::kernel::GaussianKernel" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::kernel::GaussianKernel \- 
.PP
The standard Gaussian kernel\&.  

.SH SYNOPSIS
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.PP
.SS "Public Member Functions"

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.RI "\fBGaussianKernel\fP ()"
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.RI "\fIDefault constructor; sets bandwidth to 1\&.0\&. \fP"
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.RI "\fBGaussianKernel\fP (const double \fBbandwidth\fP)"
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.RI "\fIConstruct the Gaussian kernel with a custom bandwidth\&. \fP"
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.RI "double \fBBandwidth\fP () const "
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.RI "\fIGet the bandwidth\&. \fP"
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.RI "void \fBBandwidth\fP (const double \fBbandwidth\fP)"
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.RI "\fIModify the bandwidth\&. \fP"
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.RI "template<typename VecType > double \fBConvolutionIntegral\fP (const VecType &a, const VecType &b)"
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.RI "\fIObtain a convolution integral of the Gaussian kernel\&. \fP"
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.RI "template<typename VecType > double \fBEvaluate\fP (const VecType &a, const VecType &b) const "
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.RI "\fIEvaluation of the Gaussian kernel\&. \fP"
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.RI "double \fBEvaluate\fP (const double t) const "
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.RI "\fIEvaluation of the Gaussian kernel given the distance between two points\&. \fP"
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.RI "double \fBGamma\fP () const "
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.RI "\fIGet the precalculated constant\&. \fP"
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.RI "double \fBNormalizer\fP (const size_t dimension)"
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.RI "\fIObtain the normalization constant of the Gaussian kernel\&. \fP"
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.RI "std::string \fBToString\fP () const "
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.RI "\fIConvert object to string\&. \fP"
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.SS "Private Attributes"

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.RI "double \fBbandwidth\fP"
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.RI "\fIKernel bandwidth\&. \fP"
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.RI "double \fBgamma\fP"
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.RI "\fIPrecalculated constant depending on the bandwidth; $ \gamma = -\frac{1}{2 \mu^2} $\&. \fP"
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.SH "Detailed Description"
.PP 
The standard Gaussian kernel\&. 

Given two vectors $ x $, $ y $, and a bandwidth $ \mu $ (set in the constructor),
.PP
\[ K(x, y) = \exp(-\frac{|| x - y ||^2}{2 \mu^2}). \].PP
The implementation is all in the header file because it is so simple\&. 
.PP
Definition at line 43 of file gaussian_kernel\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "mlpack::kernel::GaussianKernel::GaussianKernel ()\fC [inline]\fP"

.PP
Default constructor; sets bandwidth to 1\&.0\&. 
.PP
Definition at line 49 of file gaussian_kernel\&.hpp\&.
.SS "mlpack::kernel::GaussianKernel::GaussianKernel (const doublebandwidth)\fC [inline]\fP"

.PP
Construct the Gaussian kernel with a custom bandwidth\&. 
.PP
\fBParameters:\fP
.RS 4
\fIbandwidth\fP The bandwidth of the kernel ( $\mu$)\&. 
.RE
.PP

.PP
Definition at line 57 of file gaussian_kernel\&.hpp\&.
.SH "Member Function Documentation"
.PP 
.SS "double mlpack::kernel::GaussianKernel::Bandwidth () const\fC [inline]\fP"

.PP
Get the bandwidth\&. 
.PP
Definition at line 120 of file gaussian_kernel\&.hpp\&.
.PP
References bandwidth\&.
.SS "void mlpack::kernel::GaussianKernel::Bandwidth (const doublebandwidth)\fC [inline]\fP"

.PP
Modify the bandwidth\&. This takes an argument because we must update the precalculated constant (gamma)\&. 
.PP
Definition at line 124 of file gaussian_kernel\&.hpp\&.
.PP
References bandwidth, and gamma\&.
.SS "template<typename VecType > double mlpack::kernel::GaussianKernel::ConvolutionIntegral (const VecType &a, const VecType &b)\fC [inline]\fP"

.PP
Obtain a convolution integral of the Gaussian kernel\&. 
.PP
\fBParameters:\fP
.RS 4
\fIa,first\fP vector 
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\fIb,second\fP vector 
.RE
.PP
\fBReturns:\fP
.RS 4
the convolution integral 
.RE
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.PP
Definition at line 112 of file gaussian_kernel\&.hpp\&.
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References Evaluate(), mlpack::metric::LMetric< Power, TakeRoot >::Evaluate(), and Normalizer()\&.
.SS "template<typename VecType > double mlpack::kernel::GaussianKernel::Evaluate (const VecType &a, const VecType &b) const\fC [inline]\fP"

.PP
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\&.
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\fBTemplate Parameters:\fP
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\fIVecType\fP Type of vector (likely arma::vec or arma::spvec)\&. 
.RE
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\fBParameters:\fP
.RS 4
\fIa\fP First vector\&. 
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\fIb\fP Second vector\&. 
.RE
.PP
\fBReturns:\fP
.RS 4
K(a, b) using the bandwidth ( $\mu$) specified in the constructor\&. 
.RE
.PP

.PP
Definition at line 74 of file gaussian_kernel\&.hpp\&.
.PP
References mlpack::metric::LMetric< Power, TakeRoot >::Evaluate(), and gamma\&.
.PP
Referenced by ConvolutionIntegral()\&.
.SS "double mlpack::kernel::GaussianKernel::Evaluate (const doublet) const\fC [inline]\fP"

.PP
Evaluation of the Gaussian kernel given the distance between two points\&. 
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\fBParameters:\fP
.RS 4
\fIt\fP The distance between the two points the kernel is evaluated on\&. 
.RE
.PP
\fBReturns:\fP
.RS 4
K(t) using the bandwidth ( $\mu$) specified in the constructor\&. 
.RE
.PP

.PP
Definition at line 87 of file gaussian_kernel\&.hpp\&.
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References gamma\&.
.SS "double mlpack::kernel::GaussianKernel::Gamma () const\fC [inline]\fP"

.PP
Get the precalculated constant\&. 
.PP
Definition at line 131 of file gaussian_kernel\&.hpp\&.
.PP
References gamma\&.
.SS "double mlpack::kernel::GaussianKernel::Normalizer (const size_tdimension)\fC [inline]\fP"

.PP
Obtain the normalization constant of the Gaussian kernel\&. 
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\fBParameters:\fP
.RS 4
\fIdimension\fP 
.RE
.PP
\fBReturns:\fP
.RS 4
the normalization constant 
.RE
.PP

.PP
Definition at line 99 of file gaussian_kernel\&.hpp\&.
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References bandwidth, and M_PI\&.
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Referenced by ConvolutionIntegral()\&.
.SS "std::string mlpack::kernel::GaussianKernel::ToString () const\fC [inline]\fP"

.PP
Convert object to string\&. 
.PP
Definition at line 134 of file gaussian_kernel\&.hpp\&.
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References bandwidth\&.
.SH "Member Data Documentation"
.PP 
.SS "double mlpack::kernel::GaussianKernel::bandwidth\fC [private]\fP"

.PP
Kernel bandwidth\&. 
.PP
Definition at line 144 of file gaussian_kernel\&.hpp\&.
.PP
Referenced by Bandwidth(), Normalizer(), and ToString()\&.
.SS "double mlpack::kernel::GaussianKernel::gamma\fC [private]\fP"

.PP
Precalculated constant depending on the bandwidth; $ \gamma = -\frac{1}{2 \mu^2} $\&. 
.PP
Definition at line 148 of file gaussian_kernel\&.hpp\&.
.PP
Referenced by Bandwidth(), Evaluate(), and Gamma()\&.

.SH "Author"
.PP 
Generated automatically by Doxygen for MLPACK from the source code\&.