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‎documentation/html/_formulas.tex‎

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\documentclass{article}
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\usepackage{ifthen}
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\usepackage{epsfig}
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\usepackage[utf8]{inputenc}
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\usepackage{newunicodechar}
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\newunicodechar{⁻}{${}^{-}$}% Superscript minus
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\newunicodechar{²}{${}^{2}$}% Superscript two
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\newunicodechar{³}{${}^{3}$}% Superscript three
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\pagestyle{empty}
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\begin{document}
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\[ \mathcal{P}(\phi_t^\mathcal{O}|\phi_t^\mathcal{I}) \sim \sum_{i=1}^K h_i(\phi_t^\mathcal{I}) \mathcal{N}\left(\hat{\mu}_t^\mathcal{O}(\phi_t^\mathcal{I}), \hat{\Sigma}_t^\mathcal{O}\right) \]
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\pagebreak
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\[ \hat{\mu}_i^\mathcal{O}(\phi_t^\mathcal{I}) = \mu_i^\mathcal{O} + \Sigma_i^\mathcal{OI}\Sigma_i^{\mathcal{I}, -1}(\phi_t^\mathcal{I} - \mu_i^\mathcal{I}) \]
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\pagebreak
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\[ \hat{\Sigma}_t^\mathcal{O} = \Sigma_i^\mathcal{O} - \Sigma_i^\mathcal{OI}\Sigma_i^{\mathcal{I}, -1}\Sigma_i^\mathcal{OI} \]
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\pagebreak
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\[ h_i(\phi_t^\mathcal{I}) = \frac{\pi_i \mathcal{N}(\phi_t^\mathcal{I} \mid \mu_i^\mathcal{I}, \Sigma_i^\mathcal{I})}{\sum_k^K \pi_k \mathcal{N}\mathcal(\phi_t^\mathcal{I} \mid \mu_k^\mathcal{I}, \Sigma_k^\mathcal{I})} \]
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\pagebreak
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$\mu^\mathcal{I}$
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\pagebreak
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$\mu^\mathcal{O}$
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\pagebreak
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\[ \Sigma = [[\Sigma^\mathcal{I}, \Sigma^\mathcal{IO}], [\Sigma^\mathcal{OI}, \Sigma^\mathcal{O}]] \]
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\pagebreak
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$\Sigma^\mathcal{I}$
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\pagebreak
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$\Sigma^\mathcal{IO}$
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\pagebreak
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$\Sigma^\mathcal{OI}$
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\pagebreak
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$\Sigma^\mathcal{O}$
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\pagebreak
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\[ h_{t, i} = \frac{\pi_i \prod_{j=1}^P \mathcal{N}\left(X_t^{(j)} \mid \mu_i^{(j)}, \Sigma_i^{(j)}\right)}{\sum_{k=1}^K \pi_k \prod_{j=1}^P \mathcal{N}\left(X_t^{(j)} \mid \mu_k^{(j)}, \Sigma_k^{(j)}\right)} \]
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\pagebreak
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\[ \pi_i \leftarrow \frac{\sum_{t=1}^N h_{t, i}}{N} \]
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\pagebreak
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\[ \mu_i^{(j)} \leftarrow \frac{\sum_{t=1}^N h_{t, i} X_t^{(j)}}{\sum_{t=1}^N h_{t, i}} \]
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\pagebreak
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\[ \Sigma_i^{(j)} \leftarrow \frac{\sum_{t=1}^N h_{t, i} \left(X_t^{(j)} - \mu_i^{(j)}\right)\left(X_t^{(j)} - \mu_i^{(j)}\right)^T}{\sum_{t=1}^N h_{t, i}} \]
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\pagebreak
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\[ LL = \frac{\sum_{t=1}^N \log\left(\sum_{k=1}^K \pi_k \prod_{j=1}^J\mathcal{N}\left(X_t^{(j)} \mid \mu_k^{(j)}, \Sigma_k^{(j)}\right)\right)}{N} \]
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\pagebreak
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$N$
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\pagebreak
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$\pi$
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\pagebreak
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$i$
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$j$
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$\mu$
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$\Sigma$
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$LL$
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$LL_{t-1} - LL_t < \textit{self.tol}$
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\pagebreak
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$LL_{t}$
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\pagebreak
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\[ \mathcal{N}\left(X_t^{(j)} \mid \mu_i^{(j)}, \Sigma_i^{(j)}\right) = \frac{1}{\sqrt{(2\pi)^D|\Sigma_i^{(j)}|}} \exp \left( \frac{1}{2}(X_t^{(j)} - \mu_i^{(j)})\Sigma_i^{(j), -1}(X_t^{(j)} - \mu_i^{(j)})^T\right) \]
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\pagebreak
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\[ DB = \frac{1}{n} \sum_{i,j=1}^N \max_{j!=i} \frac{\sigma_i + \sigma_j}{d(c_i, c_j)} \]
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\pagebreak
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\end{document}

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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<div id="projectname">TPGMM
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<div class="header">
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<div class="headertitle">
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<div class="title">Class List</div> </div>
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</div><!--header-->
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<div class="contents">
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<div class="textblock">Here are the classes, structs, unions and interfaces with brief descriptions:</div><div class="directory">
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<div class="levels">[detail level <span onclick="javascript:toggleLevel(1);">1</span><span onclick="javascript:toggleLevel(2);">2</span><span onclick="javascript:toggleLevel(3);">3</span><span onclick="javascript:toggleLevel(4);">4</span>]</div><table class="directory">
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<tr id="row_0_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_0_" class="arrow" onclick="toggleFolder('0_')">&#9660;</span><span class="icona"><span class="icon">N</span></span><b>tpgmm</b></td><td class="desc"></td></tr>
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<tr id="row_0_0_"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_0_0_" class="arrow" onclick="toggleFolder('0_0_')">&#9660;</span><span class="icona"><span class="icon">N</span></span><b>gmr</b></td><td class="desc"></td></tr>
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<tr id="row_0_0_0_" class="even"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span id="arr_0_0_0_" class="arrow" onclick="toggleFolder('0_0_0_')">&#9660;</span><span class="icona"><span class="icon">N</span></span><b>gmr</b></td><td class="desc"></td></tr>
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<tr id="row_0_0_0_0_"><td class="entry"><span style="width:64px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="classtpgmm_1_1gmr_1_1gmr_1_1GaussianMixtureRegression.html" target="_self">GaussianMixtureRegression</a></td><td class="desc">This class implements a gaussian mixture regression model </td></tr>
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<tr id="row_0_1_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span id="arr_0_1_" class="arrow" onclick="toggleFolder('0_1_')">&#9660;</span><span class="icona"><span class="icon">N</span></span><b>utils</b></td><td class="desc"></td></tr>
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<tr id="row_0_1_0_"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span id="arr_0_1_0_" class="arrow" onclick="toggleFolder('0_1_0_')">&#9660;</span><span class="icona"><span class="icon">N</span></span><b>learning_modules</b></td><td class="desc"></td></tr>
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<tr id="row_0_1_0_0_" class="even"><td class="entry"><span style="width:64px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="classtpgmm_1_1utils_1_1learning__modules_1_1LearningModule.html" target="_self">LearningModule</a></td><td class="desc">Basic abstract class for a generic learning module </td></tr>
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<tr id="row_0_1_0_1_"><td class="entry"><span style="width:64px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="classtpgmm_1_1utils_1_1learning__modules_1_1RegressionModel.html" target="_self">RegressionModel</a></td><td class="desc">Basic Regression Model </td></tr>
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<tr id="row_0_1_0_2_" class="even"><td class="entry"><span style="width:64px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="classtpgmm_1_1utils_1_1learning__modules_1_1ClassificationModule.html" target="_self">ClassificationModule</a></td><td class="desc"></td></tr>
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<tr id="row_0_2_"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">C</span></span><a class="el" href="classtpgmm_1_1TPGMM.html" target="_self">TPGMM</a></td><td class="desc">This class in an implementation of the task parameterized gaussian mixture model according to Calinon Paper @https://calinon.ch/papers/Calinon-JIST2015.pdf </td></tr>
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</table>
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<div class="header">
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<div class="title">Class Index</div> </div>
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<div class="contents">
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<div class="qindex"><a class="qindex" href="#letter_C">C</a>&#160;|&#160;<a class="qindex" href="#letter_G">G</a>&#160;|&#160;<a class="qindex" href="#letter_L">L</a>&#160;|&#160;<a class="qindex" href="#letter_R">R</a>&#160;|&#160;<a class="qindex" href="#letter_T">T</a></div>
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<div class="classindex">
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<dl class="classindex even">
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<dt class="alphachar"><a name="letter_C">C</a></dt>
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<dd><a class="el" href="classtpgmm_1_1utils_1_1learning__modules_1_1ClassificationModule.html">ClassificationModule</a> (tpgmm.utils.learning_modules)</dd></dl>
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<dl class="classindex odd">
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<dt class="alphachar"><a name="letter_G">G</a></dt>
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<dd><a class="el" href="classtpgmm_1_1gmr_1_1gmr_1_1GaussianMixtureRegression.html">GaussianMixtureRegression</a> (tpgmm.gmr.gmr)</dd></dl>
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<dl class="classindex even">
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<dt class="alphachar"><a name="letter_L">L</a></dt>
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<dd><a class="el" href="classtpgmm_1_1utils_1_1learning__modules_1_1LearningModule.html">LearningModule</a> (tpgmm.utils.learning_modules)</dd></dl>
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<dl class="classindex odd">
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<dt class="alphachar"><a name="letter_R">R</a></dt>
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<dd><a class="el" href="classtpgmm_1_1utils_1_1learning__modules_1_1RegressionModel.html">RegressionModel</a> (tpgmm.utils.learning_modules)</dd></dl>
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<dl class="classindex even">
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<dt class="alphachar"><a name="letter_T">T</a></dt>
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<dd><a class="el" href="classtpgmm_1_1TPGMM.html">TPGMM</a> (tpgmm)</dd></dl>
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