192 lines
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192 lines
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<li class="navelem"><a class="el" href="namespacemlpack.html">mlpack</a></li><li class="navelem"><a class="el" href="namespacemlpack_1_1kernel.html">kernel</a></li> </ul>
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<p>Kernel functions.
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<a href="#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="nested-classes"></a>
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Classes</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1CosineDistance.html">CosineDistance</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The cosine distance (or cosine similarity). <a href="classmlpack_1_1kernel_1_1CosineDistance.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1EpanechnikovKernel.html">EpanechnikovKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The Epanechnikov kernel, defined as. <a href="classmlpack_1_1kernel_1_1EpanechnikovKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1ExampleKernel.html">ExampleKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">An example kernel function. <a href="classmlpack_1_1kernel_1_1ExampleKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1GaussianKernel.html">GaussianKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The standard Gaussian kernel. <a href="classmlpack_1_1kernel_1_1GaussianKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1HyperbolicTangentKernel.html">HyperbolicTangentKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Hyperbolic tangent kernel. <a href="classmlpack_1_1kernel_1_1HyperbolicTangentKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits.html">KernelTraits</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">This is a template class that can provide information about various kernels. <a href="classmlpack_1_1kernel_1_1KernelTraits.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits_3_01CosineDistance_01_4.html">KernelTraits< CosineDistance ></a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kernel traits for the cosine distance. <a href="classmlpack_1_1kernel_1_1KernelTraits_3_01CosineDistance_01_4.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits_3_01EpanechnikovKernel_01_4.html">KernelTraits< EpanechnikovKernel ></a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kernel traits for the Epanechnikov kernel. <a href="classmlpack_1_1kernel_1_1KernelTraits_3_01EpanechnikovKernel_01_4.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits_3_01GaussianKernel_01_4.html">KernelTraits< GaussianKernel ></a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kernel traits for the Gaussian kernel. <a href="classmlpack_1_1kernel_1_1KernelTraits_3_01GaussianKernel_01_4.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits_3_01LaplacianKernel_01_4.html">KernelTraits< LaplacianKernel ></a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kernel traits of the Laplacian kernel. <a href="classmlpack_1_1kernel_1_1KernelTraits_3_01LaplacianKernel_01_4.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits_3_01SphericalKernel_01_4.html">KernelTraits< SphericalKernel ></a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kernel traits for the spherical kernel. <a href="classmlpack_1_1kernel_1_1KernelTraits_3_01SphericalKernel_01_4.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KernelTraits_3_01TriangularKernel_01_4.html">KernelTraits< TriangularKernel ></a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Kernel traits for the triangular kernel. <a href="classmlpack_1_1kernel_1_1KernelTraits_3_01TriangularKernel_01_4.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1KMeansSelection.html">KMeansSelection</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">Implementation of the kmeans sampling scheme. <a href="classmlpack_1_1kernel_1_1KMeansSelection.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1LaplacianKernel.html">LaplacianKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The standard Laplacian kernel. <a href="classmlpack_1_1kernel_1_1LaplacianKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1LinearKernel.html">LinearKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The simple linear kernel (dot product). <a href="classmlpack_1_1kernel_1_1LinearKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1NystroemMethod.html">NystroemMethod</a></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1OrderedSelection.html">OrderedSelection</a></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1PolynomialKernel.html">PolynomialKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The simple polynomial kernel. <a href="classmlpack_1_1kernel_1_1PolynomialKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1PSpectrumStringKernel.html">PSpectrumStringKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The p-spectrum string kernel. <a href="classmlpack_1_1kernel_1_1PSpectrumStringKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1RandomSelection.html">RandomSelection</a></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1SphericalKernel.html">SphericalKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">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. <a href="classmlpack_1_1kernel_1_1SphericalKernel.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="classmlpack_1_1kernel_1_1TriangularKernel.html">TriangularKernel</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">The trivially simple triangular kernel, defined by. <a href="classmlpack_1_1kernel_1_1TriangularKernel.html#details">More...</a><br /></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>Kernel functions. </p>
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<p>This namespace contains kernel functions, which evaluate some kernel function <img class="formulaInl" alt="$ K(x, y) $" src="form_6.png"/> for some arbitrary vectors <img class="formulaInl" alt="$ x $" src="form_7.png"/> and <img class="formulaInl" alt="$ y $" src="form_8.png"/> of the same dimension. The single restriction on the function <img class="formulaInl" alt="$ K(x, y) $" src="form_6.png"/> is that it must satisfy Mercer's condition:</p>
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<p class="formulaDsp">
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<img class="formulaDsp" alt="\[ \int \int K(x, y) g(x) g(y) dx dy \ge 0 \]" src="form_9.png"/>
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</p>
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<p>for all square integrable functions <img class="formulaInl" alt="$ g(x) $" src="form_10.png"/>.</p>
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<p>The kernels in this namespace all implement the KernelType policy. For more information, see <a class="el" href="kernels.html">The KernelType policy documentation</a>. </p>
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