691 lines
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691 lines
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<p>The standard Gaussian kernel.
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<a href="classmlpack_1_1kernel_1_1GaussianKernel.html#details">More...</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
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Public Member Functions</h2></td></tr>
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<tr class="memitem:a1982249e5fbb7e4b94ae88f1e0218303"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a1982249e5fbb7e4b94ae88f1e0218303">GaussianKernel</a> ()</td></tr>
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<tr class="memdesc:a1982249e5fbb7e4b94ae88f1e0218303"><td class="mdescLeft"> </td><td class="mdescRight">Default constructor; sets bandwidth to 1.0. <a href="#a1982249e5fbb7e4b94ae88f1e0218303">More...</a><br /></td></tr>
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<tr class="separator:a1982249e5fbb7e4b94ae88f1e0218303"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab508d841b64919cd395fe5ad959c2fe5"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#ab508d841b64919cd395fe5ad959c2fe5">GaussianKernel</a> (const double <a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#abda0129ea431b857678f9c4ec9fab151">bandwidth</a>)</td></tr>
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<tr class="memdesc:ab508d841b64919cd395fe5ad959c2fe5"><td class="mdescLeft"> </td><td class="mdescRight">Construct the Gaussian kernel with a custom bandwidth. <a href="#ab508d841b64919cd395fe5ad959c2fe5">More...</a><br /></td></tr>
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<tr class="separator:ab508d841b64919cd395fe5ad959c2fe5"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a80caca0e054169dbc73aeaed0c9ce2da"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a80caca0e054169dbc73aeaed0c9ce2da">Bandwidth</a> () const </td></tr>
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<tr class="memdesc:a80caca0e054169dbc73aeaed0c9ce2da"><td class="mdescLeft"> </td><td class="mdescRight">Get the bandwidth. <a href="#a80caca0e054169dbc73aeaed0c9ce2da">More...</a><br /></td></tr>
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<tr class="separator:a80caca0e054169dbc73aeaed0c9ce2da"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ac7723e82d94352245c203b9100485ae0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#ac7723e82d94352245c203b9100485ae0">Bandwidth</a> (const double <a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#abda0129ea431b857678f9c4ec9fab151">bandwidth</a>)</td></tr>
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<tr class="memdesc:ac7723e82d94352245c203b9100485ae0"><td class="mdescLeft"> </td><td class="mdescRight">Modify the bandwidth. <a href="#ac7723e82d94352245c203b9100485ae0">More...</a><br /></td></tr>
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<tr class="separator:ac7723e82d94352245c203b9100485ae0"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a02b3cab5d575452053f69e9f69dfc47a"><td class="memTemplParams" colspan="2">template<typename VecTypeA , typename VecTypeB > </td></tr>
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<tr class="memitem:a02b3cab5d575452053f69e9f69dfc47a"><td class="memTemplItemLeft" align="right" valign="top">double </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a02b3cab5d575452053f69e9f69dfc47a">ConvolutionIntegral</a> (const VecTypeA &a, const VecTypeB &b)</td></tr>
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<tr class="memdesc:a02b3cab5d575452053f69e9f69dfc47a"><td class="mdescLeft"> </td><td class="mdescRight">Obtain a convolution integral of the Gaussian kernel. <a href="#a02b3cab5d575452053f69e9f69dfc47a">More...</a><br /></td></tr>
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<tr class="separator:a02b3cab5d575452053f69e9f69dfc47a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a574ef2113ec8ac965df031eee219dd73"><td class="memTemplParams" colspan="2">template<typename VecTypeA , typename VecTypeB > </td></tr>
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<tr class="memitem:a574ef2113ec8ac965df031eee219dd73"><td class="memTemplItemLeft" align="right" valign="top">double </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a574ef2113ec8ac965df031eee219dd73">Evaluate</a> (const VecTypeA &a, const VecTypeB &b) const </td></tr>
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<tr class="memdesc:a574ef2113ec8ac965df031eee219dd73"><td class="mdescLeft"> </td><td class="mdescRight">Evaluation of the Gaussian kernel. <a href="#a574ef2113ec8ac965df031eee219dd73">More...</a><br /></td></tr>
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<tr class="separator:a574ef2113ec8ac965df031eee219dd73"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5336c3dbf963c079757ed35fe685c39b"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a5336c3dbf963c079757ed35fe685c39b">Evaluate</a> (const double t) const </td></tr>
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<tr class="memdesc:a5336c3dbf963c079757ed35fe685c39b"><td class="mdescLeft"> </td><td class="mdescRight">Evaluation of the Gaussian kernel given the distance between two points. <a href="#a5336c3dbf963c079757ed35fe685c39b">More...</a><br /></td></tr>
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<tr class="separator:a5336c3dbf963c079757ed35fe685c39b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a7dd6194dab1f6d6562ac0be4fa00fcae"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a7dd6194dab1f6d6562ac0be4fa00fcae">Gamma</a> () const </td></tr>
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<tr class="memdesc:a7dd6194dab1f6d6562ac0be4fa00fcae"><td class="mdescLeft"> </td><td class="mdescRight">Get the precalculated constant. <a href="#a7dd6194dab1f6d6562ac0be4fa00fcae">More...</a><br /></td></tr>
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<tr class="separator:a7dd6194dab1f6d6562ac0be4fa00fcae"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5faea1b64eff5c1e0705d560e742e2f7"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a5faea1b64eff5c1e0705d560e742e2f7">Gradient</a> (const double t) const </td></tr>
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<tr class="memdesc:a5faea1b64eff5c1e0705d560e742e2f7"><td class="mdescLeft"> </td><td class="mdescRight">Evaluation of the gradient of Gaussian kernel given the distance between two points. <a href="#a5faea1b64eff5c1e0705d560e742e2f7">More...</a><br /></td></tr>
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<tr class="separator:a5faea1b64eff5c1e0705d560e742e2f7"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab2bd0f1eb24fe8a7508d49fba1659942"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#ab2bd0f1eb24fe8a7508d49fba1659942">GradientForSquaredDistance</a> (const double t) const </td></tr>
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<tr class="memdesc:ab2bd0f1eb24fe8a7508d49fba1659942"><td class="mdescLeft"> </td><td class="mdescRight">Evaluation of the gradient of Gaussian kernel given the squared distance between two points. <a href="#ab2bd0f1eb24fe8a7508d49fba1659942">More...</a><br /></td></tr>
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<tr class="separator:ab2bd0f1eb24fe8a7508d49fba1659942"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a17bc9e87e69d5187a11fa12e2f9a3ba2"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a17bc9e87e69d5187a11fa12e2f9a3ba2">Normalizer</a> (const size_t dimension)</td></tr>
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<tr class="memdesc:a17bc9e87e69d5187a11fa12e2f9a3ba2"><td class="mdescLeft"> </td><td class="mdescRight">Obtain the normalization constant of the Gaussian kernel. <a href="#a17bc9e87e69d5187a11fa12e2f9a3ba2">More...</a><br /></td></tr>
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<tr class="separator:a17bc9e87e69d5187a11fa12e2f9a3ba2"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae459d2087dbad74c8aa57515db45123b"><td class="memTemplParams" colspan="2">template<typename Archive > </td></tr>
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<tr class="memitem:ae459d2087dbad74c8aa57515db45123b"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#ae459d2087dbad74c8aa57515db45123b">Serialize</a> (Archive &ar, const unsigned int)</td></tr>
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<tr class="memdesc:ae459d2087dbad74c8aa57515db45123b"><td class="mdescLeft"> </td><td class="mdescRight">Serialize the kernel. <a href="#ae459d2087dbad74c8aa57515db45123b">More...</a><br /></td></tr>
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<tr class="separator:ae459d2087dbad74c8aa57515db45123b"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pri-attribs"></a>
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Private Attributes</h2></td></tr>
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<tr class="memitem:abda0129ea431b857678f9c4ec9fab151"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#abda0129ea431b857678f9c4ec9fab151">bandwidth</a></td></tr>
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<tr class="memdesc:abda0129ea431b857678f9c4ec9fab151"><td class="mdescLeft"> </td><td class="mdescRight">Kernel bandwidth. <a href="#abda0129ea431b857678f9c4ec9fab151">More...</a><br /></td></tr>
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<tr class="separator:abda0129ea431b857678f9c4ec9fab151"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a7f019a726e3dca20edb7721ad994fe6a"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html#a7f019a726e3dca20edb7721ad994fe6a">gamma</a></td></tr>
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<tr class="memdesc:a7f019a726e3dca20edb7721ad994fe6a"><td class="mdescLeft"> </td><td class="mdescRight">Precalculated constant depending on the bandwidth; <img class="formulaInl" alt="$ \gamma = -\frac{1}{2 \mu^2} $" src="form_13.png"/>. <a href="#a7f019a726e3dca20edb7721ad994fe6a">More...</a><br /></td></tr>
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<tr class="separator:a7f019a726e3dca20edb7721ad994fe6a"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>The standard Gaussian kernel. </p>
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<p>Given two vectors <img class="formulaInl" alt="$ x $" src="form_7.png"/>, <img class="formulaInl" alt="$ y $" src="form_8.png"/>, and a bandwidth <img class="formulaInl" alt="$ \mu $" src="form_11.png"/> (set in the constructor),</p>
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<p class="formulaDsp">
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<img class="formulaDsp" alt="\[ K(x, y) = \exp(-\frac{|| x - y ||^2}{2 \mu^2}). \]" src="form_12.png"/>
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</p>
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<p>The implementation is all in the header file because it is so simple. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00034">34</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<a class="anchor" id="a1982249e5fbb7e4b94ae88f1e0218303"></a>
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<td>(</td>
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<td class="paramname"></td><td>)</td>
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<p>Default constructor; sets bandwidth to 1.0. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00040">40</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<td class="memname">mlpack::kernel::GaussianKernel::GaussianKernel </td>
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<td>(</td>
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<td class="paramtype">const double </td>
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<td class="paramname"><em>bandwidth</em></td><td>)</td>
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<p>Construct the Gaussian kernel with a custom bandwidth. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">bandwidth</td><td>The bandwidth of the kernel ( <img class="formulaInl" alt="$\mu$" src="form_2.png"/>). </td></tr>
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</dd>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00048">48</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<td class="memname">double mlpack::kernel::GaussianKernel::Bandwidth </td>
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<td>(</td>
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<p>Get the bandwidth. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00135">135</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00158">bandwidth</a>.</p>
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<p>Modify the bandwidth. </p>
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<p>This takes an argument because we must update the precalculated constant (gamma). </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00139">139</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00158">bandwidth</a>, and <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<td class="memname">double mlpack::kernel::GaussianKernel::ConvolutionIntegral </td>
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<p>Obtain a convolution integral of the Gaussian kernel. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<dl class="section return"><dt>Returns</dt><dd>The convolution integral. </dd></dl>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00127">127</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00065">Evaluate()</a>, <a class="el" href="classmlpack_1_1metric_1_1LMetric.html#ac55458730b8e36f51d2f2a3741b77181">mlpack::metric::LMetric< TPower, TTakeRoot >::Evaluate()</a>, and <a class="el" href="gaussian__kernel_8hpp_source.html#l00114">Normalizer()</a>.</p>
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<td class="memname">double mlpack::kernel::GaussianKernel::Evaluate </td>
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<p>Evaluation of the Gaussian kernel. </p>
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<p>This could be generalized to use any distance metric, not the Euclidean distance, but for now, the Euclidean distance is used.</p>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>K(a, b) using the bandwidth ( <img class="formulaInl" alt="$\mu$" src="form_2.png"/>) specified in the constructor. </dd></dl>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00065">65</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="classmlpack_1_1metric_1_1LMetric.html#ac55458730b8e36f51d2f2a3741b77181">mlpack::metric::LMetric< TPower, TTakeRoot >::Evaluate()</a>, and <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<p>Referenced by <a class="el" href="gaussian__kernel_8hpp_source.html#l00127">ConvolutionIntegral()</a>.</p>
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<td class="memname">double mlpack::kernel::GaussianKernel::Evaluate </td>
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<p>Evaluation of the Gaussian kernel given the distance between two points. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">t</td><td>The distance between the two points the kernel is evaluated on. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>K(t) using the bandwidth ( <img class="formulaInl" alt="$\mu$" src="form_2.png"/>) specified in the constructor. </dd></dl>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00078">78</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<p>Get the precalculated constant. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00146">146</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<td class="paramtype">const double </td>
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<p>Evaluation of the gradient of Gaussian kernel given the distance between two points. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">t</td><td>The distance between the two points the kernel is evaluated on. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>K(t) using the bandwidth ( <img class="formulaInl" alt="$\mu$" src="form_2.png"/>) specified in the constructor. </dd></dl>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00092">92</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<td class="memname">double mlpack::kernel::GaussianKernel::GradientForSquaredDistance </td>
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<td class="paramtype">const double </td>
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<p>Evaluation of the gradient of Gaussian kernel given the squared distance between two points. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">t</td><td>The squared distance between the two points </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>K(t) using the bandwidth ( <img class="formulaInl" alt="$\mu$" src="form_2.png"/>) specified in the constructor. </dd></dl>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00104">104</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<td class="memname">double mlpack::kernel::GaussianKernel::Normalizer </td>
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<td>(</td>
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<td class="paramtype">const size_t </td>
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<p>Obtain the normalization constant of the Gaussian kernel. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>the normalization constant </dd></dl>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00114">114</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00158">bandwidth</a>, and <a class="el" href="prereqs_8hpp_source.html#l00040">M_PI</a>.</p>
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<p>Referenced by <a class="el" href="gaussian__kernel_8hpp_source.html#l00127">ConvolutionIntegral()</a>.</p>
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<td class="memname">void mlpack::kernel::GaussianKernel::Serialize </td>
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<p>Serialize the kernel. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00150">150</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>References <a class="el" href="gaussian__kernel_8hpp_source.html#l00158">bandwidth</a>, <a class="el" href="serialization__shim_8hpp_source.html#l00094">mlpack::data::CreateNVP()</a>, and <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">gamma</a>.</p>
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<h2 class="groupheader">Member Data Documentation</h2>
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<td class="memname">double mlpack::kernel::GaussianKernel::bandwidth</td>
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<p>Kernel bandwidth. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00158">158</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>Referenced by <a class="el" href="gaussian__kernel_8hpp_source.html#l00135">Bandwidth()</a>, <a class="el" href="gaussian__kernel_8hpp_source.html#l00114">Normalizer()</a>, and <a class="el" href="gaussian__kernel_8hpp_source.html#l00150">Serialize()</a>.</p>
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<span class="mlabels"><span class="mlabel">private</span></span> </td>
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<p>Precalculated constant depending on the bandwidth; <img class="formulaInl" alt="$ \gamma = -\frac{1}{2 \mu^2} $" src="form_13.png"/>. </p>
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<p>Definition at line <a class="el" href="gaussian__kernel_8hpp_source.html#l00162">162</a> of file <a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a>.</p>
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<p>Referenced by <a class="el" href="gaussian__kernel_8hpp_source.html#l00139">Bandwidth()</a>, <a class="el" href="gaussian__kernel_8hpp_source.html#l00065">Evaluate()</a>, <a class="el" href="gaussian__kernel_8hpp_source.html#l00146">Gamma()</a>, <a class="el" href="gaussian__kernel_8hpp_source.html#l00092">Gradient()</a>, <a class="el" href="gaussian__kernel_8hpp_source.html#l00104">GradientForSquaredDistance()</a>, and <a class="el" href="gaussian__kernel_8hpp_source.html#l00150">Serialize()</a>.</p>
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<hr/>The documentation for this class was generated from the following file:<ul>
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<li>src/mlpack/core/kernels/<a class="el" href="gaussian__kernel_8hpp_source.html">gaussian_kernel.hpp</a></li>
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