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<meta property="og:description" content="A modeling tool dedicated to biological network modeling (Bertrand and others 2020, <doi:10.1093/bioinformatics/btaa855>). It allows for single or joint modeling of, for instance, genes and proteins. It starts with the selection of the actors that will be the used in the reverse engineering upcoming step. An actor can be included in that selection based on its differential measurement (for instance gene expression or protein abundance) or on its time course profile. Wrappers for actors clustering functions and cluster analysis are provided. It also allows reverse engineering of biological networks taking into account the observed time course patterns of the actors. Many inference functions are provided and dedicated to get specific features for the inferred network such as sparsity, robust links, high confidence links or stable through resampling links. Some simulation and prediction tools are also available for cascade networks (Jung and others 2014, <doi:10.1093/bioinformatics/btt705>). Example of use with microarray or RNA-Seq data are provided.">
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<div id="patterns-" class="section level1">
<div class="page-header"><h1 class="hasAnchor">
<a href="#patterns-" class="anchor"></a>Patterns <img src="reference/figures/logo.png" align="right" width="200">
</h1></div>
</div>
<div id="a-modeling-tool-dedicated-to-biological-network-modeling-to-decipher-biological-networks-with-patterned-heterogeneous-eg-multiomics-measurements" class="section level1">
<h1 class="hasAnchor">
<a href="#a-modeling-tool-dedicated-to-biological-network-modeling-to-decipher-biological-networks-with-patterned-heterogeneous-eg-multiomics-measurements" class="anchor"></a>A modeling tool dedicated to biological network modeling to decipher Biological Networks with Patterned Heterogeneous (e.g. multiOmics) Measurements</h1>
<div id="frédéric-bertrand-and-myriam-maumy-bertrand" class="section level2">
<h2 class="hasAnchor">
<a href="#fr%C3%A9d%C3%A9ric-bertrand-and-myriam-maumy-bertrand" class="anchor"></a>Frédéric Bertrand and Myriam Maumy-Bertrand</h2>
<!-- badges: start -->
<p>It is designed to work with <strong>patterned data</strong>. Famous examples of problems related to patterned data are:</p>
<ul>
<li>recovering <strong>signals</strong> in networks after a <strong>stimulation</strong> (cascade network reverse engineering),</li>
<li>analysing <strong>periodic signals</strong>.</li>
</ul>
<p>It allows for <strong>single</strong> or <strong>joint modeling</strong> of, for instance, genes and proteins.</p>
<ul>
<li>It starts with the <strong>selection of the actors</strong> that will be the used in the reverse engineering upcoming step. An actor can be included in that selection based on its <strong>differential effects</strong> (for instance gene expression or protein abundance) or on its <strong>time course profile</strong>.</li>
<li>Wrappers for <strong>actors clustering</strong> functions and cluster analysis are provided.</li>
<li>It also allows <strong>reverse engineering</strong> of biological networks taking into account the observed time course patterns of the actors. Interactions between clusters of actors can be set by the user. Any number of clusters can be activated at a single time.</li>
<li>Many <strong>inference functions</strong> are provided with the <code>Patterns</code> package and dedicated to get <strong>specific features</strong> for the inferred network such as <strong>sparsity</strong>, <strong>robust links</strong>, <strong>high confidence links</strong> or <strong>stable through resampling links</strong>.
<ul>
<li>
<strong>lasso</strong>, from the <code>lars</code> package</li>
<li>
<strong>lasso</strong>, from the <code>glmnet</code> package. An unweighted and a weighted version of the algorithm are available</li>
<li>
<strong>spls</strong>, from the <code>spls</code> package</li>
<li>
<strong>elasticnet</strong>, from the <code>elasticnet</code> package</li>
<li>
<strong>stability selection</strong>, from the <code>c060</code> package implementation of stability selection</li>
<li>
<strong>weighted stability selection</strong>, a new weighted version of the <code>c060</code> package implementation of stability selection that I created for the package</li>
<li>
<strong>robust</strong>, lasso from the <code>lars</code> package with light random Gaussian noise added to the explanatory variables</li>
<li>
<strong>selectboost</strong>, from the <code>selectboost</code> package. The selectboost algorithm looks for the more stable links against resampling that takes into account the correlated structure of the predictors</li>
<li>
<strong>weighted selectboost</strong>, a new weighted version of the <code>selectboost</code>.</li>
</ul>
</li>
<li>Some <strong>simulation</strong> and <strong>prediction</strong> tools are also available for cascade networks.</li>
<li>Examples of use with microarray or RNA-Seq data are provided.</li>
</ul>
<p>The weights are viewed as a penalty factors in the penalized regression model: it is a number that multiplies the lambda value in the minimization problem to allow differential shrinkage, <a href="https://web.stanford.edu/~hastie/Papers/glmnet.pdf">Friedman et al. 2010</a>, equation 1 page 3. If equal to 0, it implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables. Infinity means that the variable is excluded from the model. Note that the weights are rescaled to sum to the number of variables.</p>
<p>A word for those that have been using our seminal work, the <code>Cascade</code> package that we created several years ago and that was a very efficient network reverse engineering tool for cascade networks (Jung, N., Bertrand, F., Bahram, S., Vallat, L., and Maumy-Bertrand, M. (2014), <a href="https://doi.org/10.1093/bioinformatics/btt705" class="uri">https://doi.org/10.1093/bioinformatics/btt705</a>, <a href="https://cran.r-project.org/package=Cascade" class="uri">https://cran.r-project.org/package=Cascade</a>, <a href="https://github.com/fbertran/Cascade" class="uri">https://github.com/fbertran/Cascade</a> and <a href="https://fbertran.github.io/Cascade/" class="uri">https://fbertran.github.io/Cascade/</a>).</p>
<p>The <code>Patterns</code> package is more than (at least) a threeway major extension of the <code>Cascade</code> package :</p>
<ul>
<li>
<strong>any number of groups</strong> can be used whereas in the <code>Cascade</code> package only 1 group for each timepoint could be created, which prevented the users to create homogeneous clusters of genes in datasets that featured more than a few dozens of genes.</li>
<li>
<strong>custom</strong> <span class="math inline"><em>F</em></span> matrices shapes whereas in the <code>Cascade</code> package only 1 shape was provided:
<ul>
<li>interaction between groups</li>
<li>custom design of inner cells of the <span class="math inline"><em>F</em></span> matrix</li>
</ul>
</li>
<li>the custom <span class="math inline"><em>F</em></span> matrices allow to deal with <strong>heteregeneous networks</strong> with several kinds of actors such as mixing genes and proteins in a single network to perform <strong>joint inference</strong>.</li>
<li>about <strong>nine inference algorithms</strong> are provided, whereas 1 (lasso) in <code>Cascade</code>.</li>
</ul>
<p>Hence the <code>Patterns</code> package should be viewed more as a completely new modelling tools than as an extension of the <code>Cascade</code> package.</p>
<p>This website and these examples were created by F. Bertrand and M. Maumy-Bertrand.</p>
</div>
<div id="installation" class="section level2">
<h2 class="hasAnchor">
<a href="#installation" class="anchor"></a>Installation</h2>
<p>You can install the released version of Patterns from <a href="https://CRAN.R-project.org">CRAN</a> with:</p>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html">install.packages</a></span><span class="op">(</span><span class="st">"Patterns"</span><span class="op">)</span></code></pre></div>
<p>You can install the development version of Patterns from <a href="https://github.com">github</a> with:</p>
<div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">devtools</span><span class="fu">::</span><span class="fu"><a href="https://devtools.r-lib.org//reference/remote-reexports.html">install_github</a></span><span class="op">(</span><span class="st">"fbertran/Patterns"</span><span class="op">)</span></code></pre></div>
</div>
<div id="examples" class="section level2">
<h2 class="hasAnchor">
<a href="#examples" class="anchor"></a>Examples</h2>
<div id="data-management" class="section level3">
<h3 class="hasAnchor">
<a href="#data-management" class="anchor"></a>Data management</h3>
<p>Import Cascade Data (repeated measurements on several subjects) from the CascadeData package and turn them into a micro array object. The second line makes sure the CascadeData package is installed.</p>
<div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://fbertran.github.io/Patterns/">Patterns</a></span><span class="op">)</span></code></pre></div>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="kw">if</span><span class="op">(</span><span class="op">!</span><span class="kw"><a href="https://rdrr.io/r/base/library.html">require</a></span><span class="op">(</span><span class="va"><a href="http://www-irma.u-strasbg.fr/~fbertran/">CascadeData</a></span><span class="op">)</span><span class="op">)</span><span class="op">{</span><span class="fu"><a href="https://rdrr.io/r/utils/install.packages.html">install.packages</a></span><span class="op">(</span><span class="st">"CascadeData"</span><span class="op">)</span><span class="op">}</span>
<span class="fu"><a href="https://rdrr.io/r/utils/data.html">data</a></span><span class="op">(</span><span class="va">micro_US</span><span class="op">)</span>
<span class="va">micro_US</span><span class="op"><-</span><span class="fu"><a href="reference/as.micro_array.html">as.micro_array</a></span><span class="op">(</span><span class="va">micro_US</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">100</span>,<span class="op">]</span>,time<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">60</span>,<span class="fl">90</span>,<span class="fl">210</span>,<span class="fl">390</span><span class="op">)</span>,subject<span class="op">=</span><span class="fl">6</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/utils/str.html">str</a></span><span class="op">(</span><span class="va">micro_US</span><span class="op">)</span>
<span class="co">#> Formal class 'micro_array' [package "Patterns"] with 7 slots</span>
<span class="co">#> ..@ microarray: num [1:100, 1:24] 103.2 26 70.7 213.7 13.7 ...</span>
<span class="co">#> .. ..- attr(*, "dimnames")=List of 2</span>
<span class="co">#> .. .. ..$ : chr [1:100] "1007_s_at" "1053_at" "117_at" "121_at" ...</span>
<span class="co">#> .. .. ..$ : chr [1:24] "N1_US_T60" "N1_US_T90" "N1_US_T210" "N1_US_T390" ...</span>
<span class="co">#> ..@ name : chr [1:100] "1007_s_at" "1053_at" "117_at" "121_at" ...</span>
<span class="co">#> ..@ gene_ID : num 0</span>
<span class="co">#> ..@ group : num 0</span>
<span class="co">#> ..@ start_time: num 0</span>
<span class="co">#> ..@ time : num [1:4] 60 90 210 390</span>
<span class="co">#> ..@ subject : num 6</span></code></pre></div>
<p>Get a summay and plots of the data:</p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">micro_US</span><span class="op">)</span>
<span class="co">#> N1_US_T60 N1_US_T90 N1_US_T210 </span>
<span class="co">#> Min. : 12.2 Min. : 12.9 Min. : 1.5 </span>
<span class="co">#> 1st Qu.: 177.7 1st Qu.: 198.7 1st Qu.: 189.0 </span>
<span class="co">#> Median : 513.0 Median : 499.4 Median : 608.5 </span>
<span class="co">#> Mean :1386.6 Mean :1357.7 Mean :1450.4 </span>
<span class="co">#> 3rd Qu.:1912.3 3rd Qu.:1883.4 3rd Qu.:2050.2 </span>
<span class="co">#> Max. :6348.4 Max. :6507.3 Max. :6438.5 </span>
<span class="co">#> N1_US_T390 N2_US_T60 N2_US_T90 </span>
<span class="co">#> Min. : 10.1 Min. : 16.7 Min. : 3.4 </span>
<span class="co">#> 1st Qu.: 196.7 1st Qu.: 212.4 1st Qu.: 185.7 </span>
<span class="co">#> Median : 541.2 Median : 584.1 Median : 501.5 </span>
<span class="co">#> Mean :1331.2 Mean :1381.9 Mean :1345.4 </span>
<span class="co">#> 3rd Qu.:1646.2 3rd Qu.:1616.2 3rd Qu.:1830.5 </span>
<span class="co">#> Max. :6351.4 Max. :6149.3 Max. :6090.8 </span>
<span class="co">#> N2_US_T210 N2_US_T390 N3_US_T60 </span>
<span class="co">#> Min. : 5.5 Min. : 6.1 Min. : 1.9 </span>
<span class="co">#> 1st Qu.: 214.7 1st Qu.: 230.1 1st Qu.: 187.4 </span>
<span class="co">#> Median : 596.0 Median : 601.8 Median : 611.4 </span>
<span class="co">#> Mean :1410.5 Mean :1403.7 Mean :1365.4 </span>
<span class="co">#> 3rd Qu.:2005.8 3rd Qu.:1901.7 3rd Qu.:1855.2 </span>
<span class="co">#> Max. :6160.6 Max. :6143.1 Max. :6636.6 </span>
<span class="co">#> N3_US_T90 N3_US_T210 N3_US_T390 </span>
<span class="co">#> Min. : 10.3 Min. : 3.3 Min. : 6.6 </span>
<span class="co">#> 1st Qu.: 194.6 1st Qu.: 177.8 1st Qu.: 222.6 </span>
<span class="co">#> Median : 576.2 Median : 552.2 Median : 593.7 </span>
<span class="co">#> Mean :1381.2 Mean :1310.1 Mean :1427.1 </span>
<span class="co">#> 3rd Qu.:2040.2 3rd Qu.:1784.5 3rd Qu.:2131.7 </span>
<span class="co">#> Max. :6515.5 Max. :6530.4 Max. :6177.2 </span>
<span class="co">#> N4_US_T60 N4_US_T90 N4_US_T210 </span>
<span class="co">#> Min. : 20.2 Min. : 15.6 Min. : 19.8 </span>
<span class="co">#> 1st Qu.: 199.3 1st Qu.: 215.4 1st Qu.: 207.0 </span>
<span class="co">#> Median : 610.8 Median : 614.0 Median : 544.9 </span>
<span class="co">#> Mean :1505.1 Mean :1526.7 Mean :1401.6 </span>
<span class="co">#> 3rd Qu.:2198.1 3rd Qu.:2168.9 3rd Qu.:1831.2 </span>
<span class="co">#> Max. :6986.2 Max. :7148.0 Max. :6820.0 </span>
<span class="co">#> N4_US_T390 N5_US_T60 N5_US_T90 </span>
<span class="co">#> Min. : 9.3 Min. : 3.4 Min. : 10.0 </span>
<span class="co">#> 1st Qu.: 197.8 1st Qu.: 213.2 1st Qu.: 209.8 </span>
<span class="co">#> Median : 590.7 Median : 609.4 Median : 561.3 </span>
<span class="co">#> Mean :1458.8 Mean :1498.2 Mean :1424.8 </span>
<span class="co">#> 3rd Qu.:1984.8 3rd Qu.:2008.7 3rd Qu.:1906.5 </span>
<span class="co">#> Max. :6762.3 Max. :7268.2 Max. :6857.8 </span>
<span class="co">#> N5_US_T210 N5_US_T390 N6_US_T60 </span>
<span class="co">#> Min. : 10.7 Min. : 16.5 Min. : 13.0 </span>
<span class="co">#> 1st Qu.: 202.0 1st Qu.: 208.2 1st Qu.: 207.5 </span>
<span class="co">#> Median : 555.6 Median : 570.5 Median : 516.2 </span>
<span class="co">#> Mean :1394.1 Mean :1435.3 Mean :1412.9 </span>
<span class="co">#> 3rd Qu.:1923.9 3rd Qu.:1867.8 3rd Qu.:2037.4 </span>
<span class="co">#> Max. :6574.0 Max. :6896.6 Max. :6898.1 </span>
<span class="co">#> N6_US_T90 N6_US_T210 N6_US_T390 </span>
<span class="co">#> Min. : 6.6 Min. : 3.8 Min. : 14.4 </span>
<span class="co">#> 1st Qu.: 198.6 1st Qu.: 203.9 1st Qu.: 195.8 </span>
<span class="co">#> Median : 530.6 Median : 578.0 Median : 580.0 </span>
<span class="co">#> Mean :1388.3 Mean :1416.5 Mean :1360.8 </span>
<span class="co">#> 3rd Qu.:1889.8 3rd Qu.:2030.8 3rd Qu.:1872.6 </span>
<span class="co">#> Max. :6749.4 Max. :6490.0 Max. :6780.2</span></code></pre></div>
<p><img src="reference/figures/README-plotmicroarrayclass-1.png" title="plot of chunk plotmicroarrayclass" alt="plot of chunk plotmicroarrayclass" width="100%"><img src="reference/figures/README-plotmicroarrayclass-2.png" title="plot of chunk plotmicroarrayclass" alt="plot of chunk plotmicroarrayclass" width="100%"><img src="reference/figures/README-plotmicroarrayclass-3.png" title="plot of chunk plotmicroarrayclass" alt="plot of chunk plotmicroarrayclass" width="100%"></p>
<div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">micro_US</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotmicroarrayclass-4.png" title="plot of chunk plotmicroarrayclass" alt="plot of chunk plotmicroarrayclass" width="100%"></p>
</div>
<div id="gene-selection" class="section level3">
<h3 class="hasAnchor">
<a href="#gene-selection" class="anchor"></a>Gene selection</h3>
<p>There are several functions to carry out gene selection before the inference. They are detailed in the vignette of the package.</p>
</div>
<div id="data-simulation" class="section level3">
<h3 class="hasAnchor">
<a href="#data-simulation" class="anchor"></a>Data simulation</h3>
<p>Let’s simulate some cascade data and then do some reverse engineering.</p>
<p>We first design the F matrix for <span class="math inline"><em>T</em><sub><em>i</em></sub> = 4</span> times and <span class="math inline"><em>N</em><em>g</em><em>r</em><em>p</em> = 4</span> groups. The <code>Fmat</code>object is an array of sizes <span class="math inline">(<em>T</em><sub><em>i</em></sub>, <em>T</em> − <em>i</em>, <em>N</em><em>g</em><em>r</em><em>p</em><sup>2</sup>) = (4, 4, 16)</span>.</p>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Ti</span><span class="op"><-</span><span class="fl">4</span>
<span class="va">Ngrp</span><span class="op"><-</span><span class="fl">4</span>
<span class="va">Fmat</span><span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/array.html">array</a></span><span class="op">(</span><span class="fl">0</span>,dim<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">Ti</span>,<span class="va">Ngrp</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span><span class="op">)</span>
<span class="kw">for</span><span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="op">(</span><span class="va">Ti</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span><span class="op">)</span><span class="op">{</span>
<span class="kw">if</span><span class="op">(</span><span class="op">(</span><span class="op">(</span><span class="va">i</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span> <span class="op">%%</span> <span class="va">Ti</span><span class="op">)</span> <span class="op">></span> <span class="op">(</span><span class="va">i</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span> <span class="op">%/%</span> <span class="va">Ti</span><span class="op">)</span><span class="op">{</span>
<span class="va">Fmat</span><span class="op">[</span>,,<span class="va">i</span><span class="op">]</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/outer.html">outer</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="va">Ti</span>,<span class="fl">1</span><span class="op">:</span><span class="va">Ti</span>,<span class="kw">function</span><span class="op">(</span><span class="va">x</span>,<span class="va">y</span><span class="op">)</span><span class="op">{</span><span class="fl">0</span><span class="op"><</span><span class="op">(</span><span class="va">x</span><span class="op">-</span><span class="va">y</span><span class="op">)</span> <span class="op">&</span> <span class="op">(</span><span class="va">x</span><span class="op">-</span><span class="va">y</span><span class="op">)</span><span class="op"><</span><span class="fl">2</span><span class="op">}</span><span class="op">)</span><span class="op">]</span><span class="op"><-</span><span class="fl">1</span>
<span class="op">}</span>
<span class="op">}</span></code></pre></div>
<p>The <code>Patterns</code> function <code>CascadeFinit</code> is an utility function to easily define such an F matrix.</p>
<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Fbis</span><span class="op">=</span><span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/CascadeFinit.html">CascadeFinit</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">Ngrp</span>,low.trig<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/utils/str.html">str</a></span><span class="op">(</span><span class="va">Fbis</span><span class="op">)</span>
<span class="co">#> num [1:4, 1:4, 1:16] 0 0 0 0 0 0 0 0 0 0 ...</span></code></pre></div>
<p>Check if the two matrices <code>Fmat</code> and <code>Fbis</code> are identical.</p>
<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/all.html">all</a></span><span class="op">(</span><span class="va">Fmat</span><span class="op">==</span><span class="va">Fbis</span><span class="op">)</span><span class="op">)</span>
<span class="co">#> [1] TRUE</span></code></pre></div>
<p>End of F matrix definition.</p>
<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Fmat</span><span class="op">[</span>,,<span class="fl">3</span><span class="op">]</span><span class="op"><-</span><span class="va">Fmat</span><span class="op">[</span>,,<span class="fl">3</span><span class="op">]</span><span class="op">*</span><span class="fl">0.2</span>
<span class="va">Fmat</span><span class="op">[</span><span class="fl">3</span>,<span class="fl">1</span>,<span class="fl">3</span><span class="op">]</span><span class="op"><-</span><span class="fl">1</span>
<span class="va">Fmat</span><span class="op">[</span><span class="fl">4</span>,<span class="fl">2</span>,<span class="fl">3</span><span class="op">]</span><span class="op"><-</span><span class="fl">1</span>
<span class="va">Fmat</span><span class="op">[</span>,,<span class="fl">4</span><span class="op">]</span><span class="op"><-</span><span class="va">Fmat</span><span class="op">[</span>,,<span class="fl">3</span><span class="op">]</span><span class="op">*</span><span class="fl">0.3</span>
<span class="va">Fmat</span><span class="op">[</span><span class="fl">4</span>,<span class="fl">1</span>,<span class="fl">4</span><span class="op">]</span><span class="op"><-</span><span class="fl">1</span>
<span class="va">Fmat</span><span class="op">[</span>,,<span class="fl">8</span><span class="op">]</span><span class="op"><-</span><span class="va">Fmat</span><span class="op">[</span>,,<span class="fl">3</span><span class="op">]</span></code></pre></div>
<p>We set the seed to make the results reproducible and draw a scale free random network.</p>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/Random.html">set.seed</a></span><span class="op">(</span><span class="fl">1</span><span class="op">)</span>
<span class="va">Net</span><span class="op"><-</span><span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/network_random.html">network_random</a></span><span class="op">(</span>
nb<span class="op">=</span><span class="fl">100</span>,
time_label<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span>,each<span class="op">=</span><span class="fl">25</span><span class="op">)</span>,
exp<span class="op">=</span><span class="fl">1</span>,
init<span class="op">=</span><span class="fl">1</span>,
regul<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/Round.html">round</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Exponential.html">rexp</a></span><span class="op">(</span><span class="fl">100</span>,<span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">+</span><span class="fl">1</span>,
min_expr<span class="op">=</span><span class="fl">0.1</span>,
max_expr<span class="op">=</span><span class="fl">2</span>,
casc.level<span class="op">=</span><span class="fl">0.4</span>
<span class="op">)</span>
<span class="va">Net</span><span class="op">@</span><span class="va">F</span><span class="op"><-</span><span class="va">Fmat</span>
<span class="fu"><a href="https://rdrr.io/r/utils/str.html">str</a></span><span class="op">(</span><span class="va">Net</span><span class="op">)</span>
<span class="co">#> Formal class 'network' [package "Patterns"] with 6 slots</span>
<span class="co">#> ..@ network: num [1:100, 1:100] 0 0 0 0 0 0 0 0 0 0 ...</span>
<span class="co">#> ..@ name : chr [1:100] "gene 1" "gene 2" "gene 3" "gene 4" ...</span>
<span class="co">#> ..@ F : num [1:4, 1:4, 1:16] 0 0 0 0 0 0 0 0 0 0 ...</span>
<span class="co">#> ..@ convF : num [1, 1] 0</span>
<span class="co">#> ..@ convO : num 0</span>
<span class="co">#> ..@ time_pt: int [1:4] 1 2 3 4</span></code></pre></div>
<p>Plot the simulated network.</p>
<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net</span>, choice<span class="op">=</span><span class="st">"network"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotnet1-1.png" title="plot of chunk plotnet1" alt="plot of chunk plotnet1" width="100%"></p>
<p>If a gene clustering is known, it can be used as a coloring scheme.</p>
<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net</span>, choice<span class="op">=</span><span class="st">"network"</span>, gr<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span>,each<span class="op">=</span><span class="fl">25</span><span class="op">)</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotnet2-1.png" title="plot of chunk plotnet2" alt="plot of chunk plotnet2" width="100%"></p>
<p>Plot the F matrix, for low dimensional F matrices.</p>
<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net</span>, choice<span class="op">=</span><span class="st">"F"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotF-1.png" title="plot of chunk plotF" alt="plot of chunk plotF" width="100%"></p>
<p>Plot the F matrix using the <code>pixmap</code> package, for high dimensional F matrices.</p>
<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net</span>, choice<span class="op">=</span><span class="st">"Fpixmap"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotFpixmap-1.png" title="plot of chunk plotFpixmap" alt="plot of chunk plotFpixmap" width="100%"></p>
<p>We simulate gene expression according to the network that was previously drawn</p>
<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/Random.html">set.seed</a></span><span class="op">(</span><span class="fl">1</span><span class="op">)</span>
<span class="va">M</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/gene_expr_simulation,network-method.html">gene_expr_simulation</a></span><span class="op">(</span>
network<span class="op">=</span><span class="va">Net</span>,
time_label<span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span>,each<span class="op">=</span><span class="fl">25</span><span class="op">)</span>,
subject<span class="op">=</span><span class="fl">5</span>,
peak_level<span class="op">=</span><span class="fl">200</span>,
act_time_group<span class="op">=</span><span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">)</span>
<span class="fu"><a href="https://rdrr.io/r/utils/str.html">str</a></span><span class="op">(</span><span class="va">M</span><span class="op">)</span>
<span class="co">#> Formal class 'micro_array' [package "Patterns"] with 7 slots</span>
<span class="co">#> ..@ microarray: num [1:100, 1:20] 86.1 -146.8 228.3 505.1 -36.6 ...</span>
<span class="co">#> .. ..- attr(*, "dimnames")=List of 2</span>
<span class="co">#> .. .. ..$ : chr [1:100] "gene 1" "gene 2" "gene 3" "gene 4" ...</span>
<span class="co">#> .. .. ..$ : chr [1:20] "log(S/US) : P1T1" "log(S/US) : P1T2" "log(S/US) : P1T3" "log(S/US) : P1T4" ...</span>
<span class="co">#> ..@ name : chr [1:100] "gene 1" "gene 2" "gene 3" "gene 4" ...</span>
<span class="co">#> ..@ gene_ID : num 0</span>
<span class="co">#> ..@ group : int [1:100] 1 1 1 1 1 1 1 1 1 1 ...</span>
<span class="co">#> ..@ start_time: num 0</span>
<span class="co">#> ..@ time : int [1:4] 1 2 3 4</span>
<span class="co">#> ..@ subject : num 5</span></code></pre></div>
<p>Get a summay and plots of the simulated data:</p>
<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/summary.html">summary</a></span><span class="op">(</span><span class="va">M</span><span class="op">)</span>
<span class="co">#> log(S/US) : P1T1 log(S/US) : P1T2 log(S/US) : P1T3 </span>
<span class="co">#> Min. :-486.823 Min. :-1962.641 Min. :-1923.74 </span>
<span class="co">#> 1st Qu.: -54.618 1st Qu.: -23.300 1st Qu.: -71.99 </span>
<span class="co">#> Median : -8.319 Median : 0.000 Median : -3.85 </span>
<span class="co">#> Mean : 8.799 Mean : 22.064 Mean : 20.72 </span>
<span class="co">#> 3rd Qu.: 69.340 3rd Qu.: 9.707 3rd Qu.: 33.00 </span>
<span class="co">#> Max. : 942.229 Max. : 1616.469 Max. : 2899.61 </span>
<span class="co">#> log(S/US) : P1T4 log(S/US) : P2T1 log(S/US) : P2T2 </span>
<span class="co">#> Min. :-3391.76 Min. :-359.82 Min. :-1126.13 </span>
<span class="co">#> 1st Qu.: -58.69 1st Qu.: -39.27 1st Qu.: -14.15 </span>
<span class="co">#> Median : 1.53 Median : 12.54 Median : 0.00 </span>
<span class="co">#> Mean : 19.82 Mean : 21.35 Mean : 20.02 </span>
<span class="co">#> 3rd Qu.: 69.45 3rd Qu.: 73.02 3rd Qu.: 28.54 </span>
<span class="co">#> Max. : 3231.17 Max. : 451.61 Max. : 946.22 </span>
<span class="co">#> log(S/US) : P2T3 log(S/US) : P2T4 log(S/US) : P3T1 </span>
<span class="co">#> Min. :-600.757 Min. :-797.980 Min. :-430.696 </span>
<span class="co">#> 1st Qu.: -49.998 1st Qu.: -73.700 1st Qu.: -65.939 </span>
<span class="co">#> Median : -7.749 Median : -9.760 Median : 1.392 </span>
<span class="co">#> Mean : 23.579 Mean : 8.361 Mean : 4.032 </span>
<span class="co">#> 3rd Qu.: 67.216 3rd Qu.: 62.297 3rd Qu.: 62.391 </span>
<span class="co">#> Max. :1869.077 Max. : 935.321 Max. : 514.510 </span>
<span class="co">#> log(S/US) : P3T2 log(S/US) : P3T3 log(S/US) : P3T4 </span>
<span class="co">#> Min. :-1003.575 Min. :-718.3926 Min. :-1211.592 </span>
<span class="co">#> 1st Qu.: -3.637 1st Qu.: -43.3783 1st Qu.: -61.300 </span>
<span class="co">#> Median : 0.000 Median : -0.3233 Median : -4.124 </span>
<span class="co">#> Mean : 11.431 Mean : 19.7553 Mean : 5.993 </span>
<span class="co">#> 3rd Qu.: 36.945 3rd Qu.: 69.6650 3rd Qu.: 62.634 </span>
<span class="co">#> Max. : 752.066 Max. :1497.5790 Max. : 1296.563 </span>
<span class="co">#> log(S/US) : P4T1 log(S/US) : P4T2 log(S/US) : P4T3 </span>
<span class="co">#> Min. :-451.370 Min. :-1113.1785 Min. :-1506.536 </span>
<span class="co">#> 1st Qu.: -44.107 1st Qu.: -8.8769 1st Qu.: -48.512 </span>
<span class="co">#> Median : 7.193 Median : 0.0000 Median : 4.243 </span>
<span class="co">#> Mean : 16.034 Mean : 0.9469 Mean : -28.544 </span>
<span class="co">#> 3rd Qu.: 62.840 3rd Qu.: 33.2306 3rd Qu.: 46.374 </span>
<span class="co">#> Max. : 657.434 Max. : 844.0070 Max. : 694.220 </span>
<span class="co">#> log(S/US) : P4T4 log(S/US) : P5T1 log(S/US) : P5T2 </span>
<span class="co">#> Min. :-446.40 Min. :-747.865 Min. :-862.59 </span>
<span class="co">#> 1st Qu.: -56.95 1st Qu.: -78.166 1st Qu.: -15.10 </span>
<span class="co">#> Median : 3.71 Median : -8.900 Median : 0.00 </span>
<span class="co">#> Mean : 28.74 Mean : -7.693 Mean : 66.20 </span>
<span class="co">#> 3rd Qu.: 64.89 3rd Qu.: 45.926 3rd Qu.: 31.74 </span>
<span class="co">#> Max. :1368.62 Max. : 960.419 Max. :1899.57 </span>
<span class="co">#> log(S/US) : P5T3 log(S/US) : P5T4 </span>
<span class="co">#> Min. :-1493.607 Min. :-1420.740 </span>
<span class="co">#> 1st Qu.: -59.853 1st Qu.: -32.799 </span>
<span class="co">#> Median : -2.776 Median : 4.008 </span>
<span class="co">#> Mean : -13.865 Mean : -12.332 </span>
<span class="co">#> 3rd Qu.: 40.324 3rd Qu.: 59.892 </span>
<span class="co">#> Max. : 770.655 Max. : 489.916</span></code></pre></div>
<p><img src="reference/figures/README-summarysimuldata-1.png" title="plot of chunk summarysimuldata" alt="plot of chunk summarysimuldata" width="100%"><img src="reference/figures/README-summarysimuldata-2.png" title="plot of chunk summarysimuldata" alt="plot of chunk summarysimuldata" width="100%"><img src="reference/figures/README-summarysimuldata-3.png" title="plot of chunk summarysimuldata" alt="plot of chunk summarysimuldata" width="100%"></p>
<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">M</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotsimuldata-1.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"><img src="reference/figures/README-plotsimuldata-2.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"><img src="reference/figures/README-plotsimuldata-3.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"><img src="reference/figures/README-plotsimuldata-4.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"><img src="reference/figures/README-plotsimuldata-5.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"><img src="reference/figures/README-plotsimuldata-6.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"><img src="reference/figures/README-plotsimuldata-7.png" title="plot of chunk plotsimuldata" alt="plot of chunk plotsimuldata" width="100%"></p>
</div>
<div id="network-inferrence" class="section level3">
<h3 class="hasAnchor">
<a href="#network-inferrence" class="anchor"></a>Network inferrence</h3>
<p>We infer the new network using subjectwise leave one out cross-validation (default setting): all measurements from the same subject are removed from the dataset). The inference is carried out with a general Fshape.</p>
<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Net_inf_P</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/inference.html">inference</a></span><span class="op">(</span><span class="va">M</span>, cv.subjects<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span>
<span class="co">#> We are at step : 1</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.01</span>
<span class="co">#> We are at step : 2</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00522</span>
<span class="co">#> We are at step : 3</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.0034</span>
<span class="co">#> We are at step : 4</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00235</span>
<span class="co">#> We are at step : 5</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00181</span>
<span class="co">#> We are at step : 6</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00142</span>
<span class="co">#> We are at step : 7</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00117</span>
<span class="co">#> We are at step : 8</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1.........................</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00098</span></code></pre></div>
<p><img src="reference/figures/README-netinfdefault-1.png" title="plot of chunk netinfdefault" alt="plot of chunk netinfdefault" width="100%"><img src="reference/figures/README-netinfdefault-2.png" title="plot of chunk netinfdefault" alt="plot of chunk netinfdefault" width="100%"></p>
<p>Plot of the inferred F matrix</p>
<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net_inf_P</span>, choice<span class="op">=</span><span class="st">"F"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-Fresults-1.png" title="plot of chunk Fresults" alt="plot of chunk Fresults" width="100%"></p>
<p>Heatmap of the inferred coefficients of the Omega matrix</p>
<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">stats</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/stats/heatmap.html">heatmap</a></span><span class="op">(</span><span class="va">Net_inf_P</span><span class="op">@</span><span class="va">network</span>, Rowv <span class="op">=</span> <span class="cn">NA</span>, Colv <span class="op">=</span> <span class="cn">NA</span>, scale<span class="op">=</span><span class="st">"none"</span>, revC<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-heatresults-1.png" title="plot of chunk heatresults" alt="plot of chunk heatresults" width="100%"></p>
<p>Default values fot the <span class="math inline"><em>F</em></span> matrices. The <code>Finit</code> matrix (starting values for the algorithm). In our case, the <code>Finit</code>object is an array of sizes <span class="math inline">(<em>T</em><sub><em>i</em></sub>, <em>T</em> − <em>i</em>, <em>N</em><em>g</em><em>r</em><em>p</em><sup>2</sup>) = (4, 4, 16)</span>.</p>
<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Ti</span><span class="op"><-</span><span class="fl">4</span>;
<span class="va">ngrp</span><span class="op"><-</span><span class="fl">4</span>
<span class="va">nF</span><span class="op"><-</span><span class="va">ngrp</span><span class="op">^</span><span class="fl">2</span>
<span class="va">Finit</span><span class="op"><-</span><span class="fu"><a href="https://rdrr.io/r/base/array.html">array</a></span><span class="op">(</span><span class="fl">0</span>,<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">Ti</span>,<span class="va">nF</span><span class="op">)</span><span class="op">)</span>
<span class="kw">for</span><span class="op">(</span><span class="va">ii</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">nF</span><span class="op">)</span><span class="op">{</span>
<span class="kw">if</span><span class="op">(</span><span class="op">(</span><span class="va">ii</span><span class="op">%%</span><span class="op">(</span><span class="va">ngrp</span><span class="op">+</span><span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">==</span><span class="fl">1</span><span class="op">)</span><span class="op">{</span>
<span class="va">Finit</span><span class="op">[</span>,,<span class="va">ii</span><span class="op">]</span><span class="op"><-</span><span class="fl">0</span>
<span class="op">}</span> <span class="kw">else</span> <span class="op">{</span>
<span class="va">Finit</span><span class="op">[</span>,,<span class="va">ii</span><span class="op">]</span><span class="op"><-</span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html">cbind</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html">rbind</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="va">Ti</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/base/diag.html">diag</a></span><span class="op">(</span><span class="fl">1</span>,<span class="va">Ti</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="va">Ti</span><span class="op">)</span><span class="op">)</span><span class="op">+</span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html">rbind</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html">cbind</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="va">Ti</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/base/diag.html">diag</a></span><span class="op">(</span><span class="fl">1</span>,<span class="va">Ti</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span><span class="op">)</span>,<span class="fu"><a href="https://rdrr.io/r/base/rep.html">rep</a></span><span class="op">(</span><span class="fl">0</span>,<span class="va">Ti</span><span class="op">)</span><span class="op">)</span>
<span class="op">}</span>
<span class="op">}</span></code></pre></div>
<p>The <code>Fshape</code> matrix (default shape for <code>F</code> matrix the algorithm). Any interaction between groups and times are permitted except the retro-actions (a group on itself, or an action at the same time for an actor on another one).</p>
<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Fshape</span><span class="op"><-</span><span class="fu"><a href="https://rdrr.io/r/base/array.html">array</a></span><span class="op">(</span><span class="st">"0"</span>,<span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">Ti</span>,<span class="va">nF</span><span class="op">)</span><span class="op">)</span>
<span class="kw">for</span><span class="op">(</span><span class="va">ii</span> <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="va">nF</span><span class="op">)</span><span class="op">{</span>
<span class="kw">if</span><span class="op">(</span><span class="op">(</span><span class="va">ii</span><span class="op">%%</span><span class="op">(</span><span class="va">ngrp</span><span class="op">+</span><span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">==</span><span class="fl">1</span><span class="op">)</span><span class="op">{</span>
<span class="va">Fshape</span><span class="op">[</span>,,<span class="va">ii</span><span class="op">]</span><span class="op"><-</span><span class="st">"0"</span>
<span class="op">}</span> <span class="kw">else</span> <span class="op">{</span>
<span class="va">lchars</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html">paste</a></span><span class="op">(</span><span class="st">"a"</span>,<span class="fl">1</span><span class="op">:</span><span class="op">(</span><span class="fl">2</span><span class="op">*</span><span class="va">Ti</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span>,sep<span class="op">=</span><span class="st">""</span><span class="op">)</span>
<span class="va">tempFshape</span><span class="op"><-</span><span class="fu"><a href="https://rdrr.io/r/base/matrix.html">matrix</a></span><span class="op">(</span><span class="st">"0"</span>,<span class="va">Ti</span>,<span class="va">Ti</span><span class="op">)</span>
<span class="kw">for</span><span class="op">(</span><span class="va">bb</span> <span class="kw">in</span> <span class="op">(</span><span class="op">-</span><span class="va">Ti</span><span class="op">+</span><span class="fl">1</span><span class="op">)</span><span class="op">:</span><span class="op">(</span><span class="va">Ti</span><span class="op">-</span><span class="fl">1</span><span class="op">)</span><span class="op">)</span><span class="op">{</span>
<span class="va">tempFshape</span><span class="op"><-</span><span class="fu"><a href="reference/replaceUp.html">replaceUp</a></span><span class="op">(</span><span class="va">tempFshape</span>,<span class="fu"><a href="https://rdrr.io/r/base/matrix.html">matrix</a></span><span class="op">(</span><span class="va">lchars</span><span class="op">[</span><span class="va">bb</span><span class="op">+</span><span class="va">Ti</span><span class="op">]</span>,<span class="va">Ti</span>,<span class="va">Ti</span><span class="op">)</span>,<span class="op">-</span><span class="va">bb</span><span class="op">)</span>
<span class="op">}</span>
<span class="va">tempFshape</span> <span class="op"><-</span> <span class="fu"><a href="reference/replaceBand.html">replaceBand</a></span><span class="op">(</span><span class="va">tempFshape</span>,<span class="fu"><a href="https://rdrr.io/r/base/matrix.html">matrix</a></span><span class="op">(</span><span class="st">"0"</span>,<span class="va">Ti</span>,<span class="va">Ti</span><span class="op">)</span>,<span class="fl">0</span><span class="op">)</span>
<span class="va">Fshape</span><span class="op">[</span>,,<span class="va">ii</span><span class="op">]</span><span class="op"><-</span><span class="va">tempFshape</span>
<span class="op">}</span>
<span class="op">}</span></code></pre></div>
<p>Any other form can be used. A “0” coefficient is missing from the model. It allows testing the best structure of an “F” matrix and even performing some significance tests of hypothses on the structure of the <span class="math inline"><em>F</em></span> matrix.</p>
<p>The <code>IndicFshape</code> function allows to design custom F matrix for cascade networks with equally spaced measurements by specifying the zero and non zero <span class="math inline"><em>F</em><sub><em>i</em><em>j</em></sub></span> cells of the <span class="math inline"><em>F</em></span> matrix. It is useful for models featuring several clusters of actors that are activated at the time. Let’s define the following indicatrix matrix (action of all groups on each other, which is not a possible real modeling setting and is only used as an example):</p>
<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">TestIndic</span><span class="op">=</span><span class="fu"><a href="https://rdrr.io/r/base/matrix.html">matrix</a></span><span class="op">(</span><span class="op">!</span><span class="op">(</span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="op">(</span><span class="va">Ti</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span><span class="op">)</span><span class="op">%%</span><span class="op">(</span><span class="va">ngrp</span><span class="op">+</span><span class="fl">1</span><span class="op">)</span><span class="op">==</span><span class="fl">1</span><span class="op">)</span>,byrow<span class="op">=</span><span class="cn">TRUE</span>,<span class="va">ngrp</span>,<span class="va">ngrp</span><span class="op">)</span>
<span class="va">TestIndic</span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] FALSE TRUE TRUE TRUE</span>
<span class="co">#> [2,] TRUE FALSE TRUE TRUE</span>
<span class="co">#> [3,] TRUE TRUE FALSE TRUE</span>
<span class="co">#> [4,] TRUE TRUE TRUE FALSE</span></code></pre></div>
<p>For that choice, we get those init and shape <span class="math inline"><em>F</em></span> matrices.</p>
<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/IndicFinit.html">IndicFinit</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">ngrp</span>,<span class="va">TestIndic</span><span class="op">)</span>
<span class="co">#> , , 1</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 0 0 0 0</span>
<span class="co">#> [3,] 0 0 0 0</span>
<span class="co">#> [4,] 0 0 0 0</span>
<span class="co">#> </span>
<span class="co">#> , , 2</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 3</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 4</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 5</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 6</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 0 0 0 0</span>
<span class="co">#> [3,] 0 0 0 0</span>
<span class="co">#> [4,] 0 0 0 0</span>
<span class="co">#> </span>
<span class="co">#> , , 7</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 8</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 9</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 10</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 11</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 0 0 0 0</span>
<span class="co">#> [3,] 0 0 0 0</span>
<span class="co">#> [4,] 0 0 0 0</span>
<span class="co">#> </span>
<span class="co">#> , , 12</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 13</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 14</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 15</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 1 0 0 0</span>
<span class="co">#> [3,] 1 1 0 0</span>
<span class="co">#> [4,] 1 1 1 0</span>
<span class="co">#> </span>
<span class="co">#> , , 16</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] 0 0 0 0</span>
<span class="co">#> [2,] 0 0 0 0</span>
<span class="co">#> [3,] 0 0 0 0</span>
<span class="co">#> [4,] 0 0 0 0</span>
<span class="fu"><a href="reference/IndicFshape.html">IndicFshape</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">ngrp</span>,<span class="va">TestIndic</span><span class="op">)</span>
<span class="co">#> , , 1</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "0" "0" "0" "0" </span>
<span class="co">#> [3,] "0" "0" "0" "0" </span>
<span class="co">#> [4,] "0" "0" "0" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 2</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 3</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 4</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 5</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 6</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "0" "0" "0" "0" </span>
<span class="co">#> [3,] "0" "0" "0" "0" </span>
<span class="co">#> [4,] "0" "0" "0" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 7</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 8</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 9</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 10</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 11</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "0" "0" "0" "0" </span>
<span class="co">#> [3,] "0" "0" "0" "0" </span>
<span class="co">#> [4,] "0" "0" "0" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 12</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 13</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 14</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 15</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "a1" "0" "0" "0" </span>
<span class="co">#> [3,] "a2" "a1" "0" "0" </span>
<span class="co">#> [4,] "a3" "a2" "a1" "0" </span>
<span class="co">#> </span>
<span class="co">#> , , 16</span>
<span class="co">#> </span>
<span class="co">#> [,1] [,2] [,3] [,4]</span>
<span class="co">#> [1,] "0" "0" "0" "0" </span>
<span class="co">#> [2,] "0" "0" "0" "0" </span>
<span class="co">#> [3,] "0" "0" "0" "0" </span>
<span class="co">#> [4,] "0" "0" "0" "0"</span></code></pre></div>
<p>Those <span class="math inline"><em>F</em></span> matrices are lower diagonal ones to enforce that an observed value at a given time can only be predicted by a value that was observed in the past only (i.e. neither at the same moment or in the future).</p>
<p>The <code>plotF</code> is convenient to display F matrices. Here are the the displays of the three <span class="math inline"><em>F</em></span> matrices we have just introduced.</p>
<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/plotF.html">plotF</a></span><span class="op">(</span><span class="va">Fshape</span>,choice<span class="op">=</span><span class="st">"Fshape"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotfshape1-1.png" title="plot of chunk plotfshape1" alt="plot of chunk plotfshape1" width="100%"></p>
<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/plotF.html">plotF</a></span><span class="op">(</span><span class="fu"><a href="reference/CascadeFshape.html">CascadeFshape</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>,choice<span class="op">=</span><span class="st">"Fshape"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotfshape2-1.png" title="plot of chunk plotfshape2" alt="plot of chunk plotfshape2" width="100%"></p>
<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="reference/plotF.html">plotF</a></span><span class="op">(</span><span class="fu"><a href="reference/IndicFshape.html">IndicFshape</a></span><span class="op">(</span><span class="va">Ti</span>,<span class="va">ngrp</span>,<span class="va">TestIndic</span><span class="op">)</span>,choice<span class="op">=</span><span class="st">"Fshape"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-plotfshape3-1.png" title="plot of chunk plotfshape3" alt="plot of chunk plotfshape3" width="100%"></p>
<p>We now fit the model with an <span class="math inline"><em>F</em></span> matrix that is designed for cascade networks.</p>
<p>Specific Fshape</p>
<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Net_inf_P_S</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/inference.html">inference</a></span><span class="op">(</span><span class="va">M</span>, Finit<span class="op">=</span><span class="fu"><a href="reference/CascadeFinit.html">CascadeFinit</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, Fshape<span class="op">=</span><span class="fu"><a href="reference/CascadeFshape.html">CascadeFshape</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span><span class="op">)</span>
<span class="co">#> We are at step : 1</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.0074</span>
<span class="co">#> We are at step : 2</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00314</span>
<span class="co">#> We are at step : 3</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.0019</span>
<span class="co">#> We are at step : 4</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00131</span>
<span class="co">#> We are at step : 5</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00101</span>
<span class="co">#> We are at step : 6</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00081</span></code></pre></div>
<p><img src="reference/figures/README-netinfLC-1.png" title="plot of chunk netinfLC" alt="plot of chunk netinfLC" width="100%"><img src="reference/figures/README-netinfLC-2.png" title="plot of chunk netinfLC" alt="plot of chunk netinfLC" width="100%"></p>
<p>Plot of the inferred F matrix</p>
<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net_inf_P_S</span>, choice<span class="op">=</span><span class="st">"F"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-FresultsLC-1.png" title="plot of chunk FresultsLC" alt="plot of chunk FresultsLC" width="100%"></p>
<p>Heatmap of the coefficients of the Omega matrix of the network. They reflect the use of a special <span class="math inline"><em>F</em></span> matrix. It is an example of an F matrix specifically designed to deal with cascade networks.</p>
<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">stats</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/stats/heatmap.html">heatmap</a></span><span class="op">(</span><span class="va">Net_inf_P_S</span><span class="op">@</span><span class="va">network</span>, Rowv <span class="op">=</span> <span class="cn">NA</span>, Colv <span class="op">=</span> <span class="cn">NA</span>, scale<span class="op">=</span><span class="st">"none"</span>, revC<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-heatresultsLC-1.png" title="plot of chunk heatresultsLC" alt="plot of chunk heatresultsLC" width="100%"></p>
<p>There are many fitting functions provided with the <code>Patterns</code> package in order to search for <strong>specific features</strong> for the inferred network such as <strong>sparsity</strong>, <strong>robust links</strong>, <strong>high confidence links</strong> or <strong>stable through resampling links</strong>. :</p>
<ul>
<li>
<strong>LASSO</strong>, from the <code>lars</code> package</li>
<li>
<strong>LASSO2</strong>, from the <code>glmnet</code> package. An unweighted and a weighted version of the algorithm are available</li>
<li>
<strong>SPLS</strong>, from the <code>spls</code> package</li>
<li>
<strong>ELASTICNET</strong>, from the <code>elasticnet</code> package</li>
<li>
<strong>stability.c060</strong>, from the <code>c060</code> package implementation of stability selection</li>
<li>
<strong>stability.c060.weighted</strong>, a new weighted version of the <code>c060</code> package implementation of stability selection</li>
<li>
<strong>robust</strong>, lasso from the <code>lars</code> package with light random Gaussian noise added to the explanatory variables</li>
<li>
<strong>selectboost.weighted</strong>, a new weighted version of the <code>selectboost</code> package implementation of the selectboost algorithm to look for the more stable links against resampling that takes into account the correlated structure of the predictors. If no weights are provided, equal weigths are for all the variables (=non weighted case).</li>
</ul>
<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Net_inf_P_Lasso2</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/inference.html">inference</a></span><span class="op">(</span><span class="va">M</span>, Finit<span class="op">=</span><span class="fu"><a href="reference/CascadeFinit.html">CascadeFinit</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, Fshape<span class="op">=</span><span class="fu"><a href="reference/CascadeFshape.html">CascadeFshape</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, fitfun<span class="op">=</span><span class="st">"LASSO2"</span><span class="op">)</span>
<span class="co">#> We are at step : 1</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.0069</span>
<span class="co">#> We are at step : 2</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00229</span>
<span class="co">#> We are at step : 3</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00153</span>
<span class="co">#> We are at step : 4</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00114</span>
<span class="co">#> We are at step : 5</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00086</span></code></pre></div>
<p><img src="reference/figures/README-netinflasso2-1.png" title="plot of chunk netinflasso2" alt="plot of chunk netinflasso2" width="100%"><img src="reference/figures/README-netinflasso2-2.png" title="plot of chunk netinflasso2" alt="plot of chunk netinflasso2" width="100%"></p>
<p>Plot of the inferred F matrix</p>
<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net_inf_P_Lasso2</span>, choice<span class="op">=</span><span class="st">"F"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-Fresultslasso2-1.png" title="plot of chunk Fresultslasso2" alt="plot of chunk Fresultslasso2" width="100%"></p>
<p>Heatmap of the coefficients of the Omega matrix of the network</p>
<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">stats</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/stats/heatmap.html">heatmap</a></span><span class="op">(</span><span class="va">Net_inf_P_Lasso2</span><span class="op">@</span><span class="va">network</span>, Rowv <span class="op">=</span> <span class="cn">NA</span>, Colv <span class="op">=</span> <span class="cn">NA</span>, scale<span class="op">=</span><span class="st">"none"</span>, revC<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-heatresultslasso2-1.png" title="plot of chunk heatresultslasso2" alt="plot of chunk heatresultslasso2" width="100%"></p>
<p>We create a weighting vector to perform weighted lasso inference.</p>
<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Weights_Net</span><span class="op">=</span><span class="fu">slot</span><span class="op">(</span><span class="va">Net</span>,<span class="st">"network"</span><span class="op">)</span>
<span class="va">Weights_Net</span><span class="op">[</span><span class="va">Net</span><span class="op">@</span><span class="va">network</span><span class="op">!=</span><span class="fl">0</span><span class="op">]</span><span class="op">=</span><span class="fl">.1</span>
<span class="va">Weights_Net</span><span class="op">[</span><span class="va">Net</span><span class="op">@</span><span class="va">network</span><span class="op">==</span><span class="fl">0</span><span class="op">]</span><span class="op">=</span><span class="fl">1000</span></code></pre></div>
<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Net_inf_P_Lasso2_Weighted</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/inference.html">inference</a></span><span class="op">(</span><span class="va">M</span>, Finit<span class="op">=</span><span class="fu"><a href="reference/CascadeFinit.html">CascadeFinit</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, Fshape<span class="op">=</span><span class="fu"><a href="reference/CascadeFshape.html">CascadeFshape</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, fitfun<span class="op">=</span><span class="st">"LASSO2"</span>, priors<span class="op">=</span><span class="va">Weights_Net</span><span class="op">)</span>
<span class="co">#> We are at step : 1</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.0075</span>
<span class="co">#> We are at step : 2</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 4e-04</span></code></pre></div>
<p><img src="reference/figures/README-netinflasso2Weighted-1.png" title="plot of chunk netinflasso2Weighted" alt="plot of chunk netinflasso2Weighted" width="100%"><img src="reference/figures/README-netinflasso2Weighted-2.png" title="plot of chunk netinflasso2Weighted" alt="plot of chunk netinflasso2Weighted" width="100%"></p>
<p>Plot of the inferred F matrix</p>
<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net_inf_P_Lasso2_Weighted</span>, choice<span class="op">=</span><span class="st">"F"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-Fresultslasso2Weighted-1.png" title="plot of chunk Fresultslasso2Weighted" alt="plot of chunk Fresultslasso2Weighted" width="100%"></p>
<p>Heatmap of the coefficients of the Omega matrix of the network</p>
<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">stats</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/stats/heatmap.html">heatmap</a></span><span class="op">(</span><span class="va">Net_inf_P_Lasso2_Weighted</span><span class="op">@</span><span class="va">network</span>, Rowv <span class="op">=</span> <span class="cn">NA</span>, Colv <span class="op">=</span> <span class="cn">NA</span>, scale<span class="op">=</span><span class="st">"none"</span>, revC<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-heatresultslasso2Weighted-1.png" title="plot of chunk heatresultslasso2Weighted" alt="plot of chunk heatresultslasso2Weighted" width="100%"></p>
<div class="sourceCode" id="cb39"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Net_inf_P_SPLS</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/inference.html">inference</a></span><span class="op">(</span><span class="va">M</span>, Finit<span class="op">=</span><span class="fu"><a href="reference/CascadeFinit.html">CascadeFinit</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, Fshape<span class="op">=</span><span class="fu"><a href="reference/CascadeFshape.html">CascadeFshape</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, fitfun<span class="op">=</span><span class="st">"SPLS"</span><span class="op">)</span>
<span class="co">#> We are at step : 1</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.0075</span>
<span class="co">#> We are at step : 2</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00229</span>
<span class="co">#> We are at step : 3</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00164</span>
<span class="co">#> We are at step : 4</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00123</span>
<span class="co">#> We are at step : 5</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00104</span>
<span class="co">#> We are at step : 6</span>
<span class="co">#> Computing Group (out of 4) : </span>
<span class="co">#> 1</span>
<span class="co">#> 2.........................</span>
<span class="co">#> 3.........................</span>
<span class="co">#> 4.........................</span>
<span class="co">#> The convergence of the network is (L1 norm) : 0.00088</span></code></pre></div>
<p><img src="reference/figures/README-netinfSPLS-1.png" title="plot of chunk netinfSPLS" alt="plot of chunk netinfSPLS" width="100%"><img src="reference/figures/README-netinfSPLS-2.png" title="plot of chunk netinfSPLS" alt="plot of chunk netinfSPLS" width="100%"></p>
<p>Plot of the inferred F matrix</p>
<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">Net_inf_P_SPLS</span>, choice<span class="op">=</span><span class="st">"F"</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-FresultsSPLS-1.png" title="plot of chunk FresultsSPLS" alt="plot of chunk FresultsSPLS" width="100%"></p>
<p>Heatmap of the coefficients of the Omega matrix of the network</p>
<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu">stats</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/stats/heatmap.html">heatmap</a></span><span class="op">(</span><span class="va">Net_inf_P_SPLS</span><span class="op">@</span><span class="va">network</span>, Rowv <span class="op">=</span> <span class="cn">NA</span>, Colv <span class="op">=</span> <span class="cn">NA</span>, scale<span class="op">=</span><span class="st">"none"</span>, revC<span class="op">=</span><span class="cn">TRUE</span><span class="op">)</span></code></pre></div>
<p><img src="reference/figures/README-heatresultsSPLS-1.png" title="plot of chunk heatresultsSPLS" alt="plot of chunk heatresultsSPLS" width="100%"></p>
<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">Net_inf_P_ELASTICNET</span> <span class="op"><-</span> <span class="fu">Patterns</span><span class="fu">::</span><span class="fu"><a href="reference/inference.html">inference</a></span><span class="op">(</span><span class="va">M</span>, Finit<span class="op">=</span><span class="fu"><a href="reference/CascadeFinit.html">CascadeFinit</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, Fshape<span class="op">=</span><span class="fu"><a href="reference/CascadeFshape.html">CascadeFshape</a></span><span class="op">(</span><span class="fl">4</span>,<span class="fl">4</span><span class="op">)</span>, fitfun<span class="op">=</span><span class="st">"ELASTICNET"</span><span class="op">)</span>
<span class="co">#> We are at step : 1</span>
<span class="co">#> Computing Group (out of 4) : </span>