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svkucheryavski committed Nov 9, 2018
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2 changes: 1 addition & 1 deletion docs/index.html
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Expand Up @@ -191,7 +191,7 @@ <h1>
<div id="header">
<h1 class="title">Getting started with mdatools for R</h1>
<h4 class="author"><em>Sergey Kucheryavskiy</em></h4>
<h4 class="date"><em>July 5, 2018</em></h4>
<h4 class="date"><em>November 9, 2018</em></h4>
</div>
<div id="introduction" class="section level1 unnumbered">
<h1>Introduction</h1>
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1 change: 1 addition & 0 deletions docs/preprocessing.html
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Expand Up @@ -221,6 +221,7 @@ <h3>Autoscaling</h3>
<span class="kw">boxplot</span>(data3, <span class="dt">main =</span> <span class="st">&#39;Mean centered and standardized&#39;</span>)
<span class="kw">boxplot</span>(data4, <span class="dt">main =</span> <span class="st">&#39;Median centered and standardized&#39;</span>)</code></pre></div>
<p><img src="_main_files/figure-html/unnamed-chunk-40-1.png" width="864" /></p>
<p>Starting form v. 0.9.0, the method has additional parameter <code>max.cov</code> which allows to avoid scaling of variables with zero or very low variation. The parameter defines a limit for coefficient of variation in percent <code>sd(x) / m(x) * 100</code> and the method will not scale variables with coefficient of variation betlow this limit. Default value for the parameter is 0 which will prevent scaling of constant variables (which is leading to <code>Inf</code> values).</p>
</div>
<div id="correction-of-spectral-baseline" class="section level3 unnumbered">
<h3>Correction of spectral baseline</h3>
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98 changes: 49 additions & 49 deletions docs/randomized-pca-algorithms.html
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Expand Up @@ -207,12 +207,12 @@ <h2>Randomized PCA algorithms</h2>
t1 =<span class="st"> </span><span class="kw">system.time</span>({m1 =<span class="st"> </span><span class="kw">pca</span>(D, <span class="dt">ncomp =</span> <span class="dv">2</span>)})
<span class="kw">show</span>(t1)</code></pre></div>
<pre><code>## user system elapsed
## 50.190 2.300 54.385</code></pre>
## 52.910 2.816 55.741</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># randomized SVD with p = 5 and q = 1</span>
t2 =<span class="st"> </span><span class="kw">system.time</span>({m2 =<span class="st"> </span><span class="kw">pca</span>(D, <span class="dt">ncomp =</span> <span class="dv">2</span>, <span class="dt">rand =</span> <span class="kw">c</span>(<span class="dv">5</span>, <span class="dv">1</span>))})
<span class="kw">show</span>(t2)</code></pre></div>
<pre><code>## user system elapsed
## 28.555 2.127 32.162</code></pre>
<pre><code>## user system elapsed
## 29.620 2.668 2310.736</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># compare variances</span>
<span class="kw">summary</span>(m1)</code></pre></div>
<pre><code>##
Expand All @@ -221,8 +221,8 @@ <h2>Randomized PCA algorithms</h2>
## Info:
##
## Eigvals Expvar Cumexpvar
## Comp 1 112.401 62.09 62.09
## Comp 2 49.869 27.55 89.64</code></pre>
## Comp 1 113.696 62.35 62.35
## Comp 2 49.957 27.40 89.74</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">summary</span>(m2)</code></pre></div>
<pre><code>##
## PCA model (class pca) summary
Expand All @@ -232,33 +232,33 @@ <h2>Randomized PCA algorithms</h2>
##
## Parameters for randomized algorithm: q = 5, p = 1
## Eigvals Expvar Cumexpvar
## Comp 1 112.401 62.09 62.09
## Comp 2 49.869 27.55 89.64</code></pre>
## Comp 1 113.696 62.35 62.35
## Comp 2 49.957 27.40 89.74</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># compare loadings</span>
<span class="kw">show</span>(m1<span class="op">$</span>loadings[<span class="dv">1</span><span class="op">:</span><span class="dv">10</span>, ])</code></pre></div>
<pre><code>## Comp 1 Comp 2
## [1,] 4.186171e-05 -7.781134e-06
## [2,] 3.904258e-02 -6.903224e-02
## [3,] 6.853590e-02 -7.490861e-02
## [4,] 8.144432e-02 -1.209039e-02
## [5,] 7.424440e-02 6.137773e-02
## [6,] 4.893136e-02 7.813859e-02
## [7,] 1.148679e-02 2.273533e-02
## [8,] -2.861022e-02 -5.353235e-02
## [9,] -6.177736e-02 -8.053437e-02
## [10,] -7.976901e-02 -3.324322e-02</code></pre>
## [1,] 2.169611e-05 7.819699e-05
## [2,] -3.884146e-02 6.928805e-02
## [3,] -6.831018e-02 7.508661e-02
## [4,] -8.137611e-02 1.246559e-02
## [5,] -7.445530e-02 -6.122070e-02
## [6,] -4.921439e-02 -7.786260e-02
## [7,] -1.169291e-02 -2.269241e-02
## [8,] 2.876378e-02 5.345657e-02
## [9,] 6.195369e-02 8.026104e-02
## [10,] 7.977416e-02 3.286764e-02</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">show</span>(m2<span class="op">$</span>loadings[<span class="dv">1</span><span class="op">:</span><span class="dv">10</span>, ])</code></pre></div>
<pre><code>## Comp 1 Comp 2
## [1,] 4.186171e-05 7.781134e-06
## [2,] 3.904258e-02 6.903224e-02
## [3,] 6.853590e-02 7.490861e-02
## [4,] 8.144432e-02 1.209039e-02
## [5,] 7.424440e-02 -6.137773e-02
## [6,] 4.893136e-02 -7.813859e-02
## [7,] 1.148679e-02 -2.273533e-02
## [8,] -2.861022e-02 5.353235e-02
## [9,] -6.177736e-02 8.053437e-02
## [10,] -7.976901e-02 3.324322e-02</code></pre>
## [1,] -2.169611e-05 7.819699e-05
## [2,] 3.884146e-02 6.928805e-02
## [3,] 6.831018e-02 7.508661e-02
## [4,] 8.137611e-02 1.246559e-02
## [5,] 7.445530e-02 -6.122070e-02
## [6,] 4.921439e-02 -7.786260e-02
## [7,] 1.169291e-02 -2.269241e-02
## [8,] -2.876378e-02 5.345657e-02
## [9,] -6.195369e-02 8.026104e-02
## [10,] -7.977416e-02 3.286764e-02</code></pre>
<p>As you can see the explained variance values, eigenvalues and loadings are identical in the two models and the second method is about twice faster.</p>
<p>It is possible to make PCA decomposition even faster if only loadings and scores are needed. In this case you can use method <code>pca.run()</code> and skip other steps, like calculation of residuals, variances, critical limits and so on. But in this case data matrix must be centered (and scaled if necessary) manually prior to the decomposition. Here is an example using the data generated in previous code.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">D =<span class="st"> </span><span class="kw">scale</span>(D, <span class="dt">center =</span> T, <span class="dt">scale =</span> F)
Expand All @@ -267,37 +267,37 @@ <h2>Randomized PCA algorithms</h2>
t1 =<span class="st"> </span><span class="kw">system.time</span>({P1 =<span class="st"> </span><span class="kw">pca.run</span>(D, <span class="dt">method =</span> <span class="st">&#39;svd&#39;</span>, <span class="dt">ncomp =</span> <span class="dv">2</span>)})
<span class="kw">show</span>(t1)</code></pre></div>
<pre><code>## user system elapsed
## 22.881 0.274 23.253</code></pre>
## 28.070 0.257 29.614</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># randomized SVD with p = 5 and q = 1</span>
t2 =<span class="st"> </span><span class="kw">system.time</span>({P2 =<span class="st"> </span><span class="kw">pca.run</span>(D, <span class="dt">method =</span> <span class="st">&#39;svd&#39;</span>, <span class="dt">ncomp =</span> <span class="dv">2</span>, <span class="dt">rand =</span> <span class="kw">c</span>(<span class="dv">5</span>, <span class="dv">1</span>))})
<span class="kw">show</span>(t2)</code></pre></div>
<pre><code>## user system elapsed
## 1.783 0.041 1.825</code></pre>
## 2.269 0.062 2.332</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># compare loadings</span>
<span class="kw">show</span>(P1<span class="op">$</span>loadings[<span class="dv">1</span><span class="op">:</span><span class="dv">10</span>, ])</code></pre></div>
<pre><code>## [,1] [,2]
## [1,] 4.186171e-05 -7.781134e-06
## [2,] 3.904258e-02 -6.903224e-02
## [3,] 6.853590e-02 -7.490861e-02
## [4,] 8.144432e-02 -1.209039e-02
## [5,] 7.424440e-02 6.137773e-02
## [6,] 4.893136e-02 7.813859e-02
## [7,] 1.148679e-02 2.273533e-02
## [8,] -2.861022e-02 -5.353235e-02
## [9,] -6.177736e-02 -8.053437e-02
## [10,] -7.976901e-02 -3.324322e-02</code></pre>
## [1,] 2.169611e-05 7.819699e-05
## [2,] -3.884146e-02 6.928805e-02
## [3,] -6.831018e-02 7.508661e-02
## [4,] -8.137611e-02 1.246559e-02
## [5,] -7.445530e-02 -6.122070e-02
## [6,] -4.921439e-02 -7.786260e-02
## [7,] -1.169291e-02 -2.269241e-02
## [8,] 2.876378e-02 5.345657e-02
## [9,] 6.195369e-02 8.026104e-02
## [10,] 7.977416e-02 3.286764e-02</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">show</span>(P2<span class="op">$</span>loadings[<span class="dv">1</span><span class="op">:</span><span class="dv">10</span>, ])</code></pre></div>
<pre><code>## [,1] [,2]
## [1,] 4.186171e-05 7.781134e-06
## [2,] 3.904258e-02 6.903224e-02
## [3,] 6.853590e-02 7.490861e-02
## [4,] 8.144432e-02 1.209039e-02
## [5,] 7.424440e-02 -6.137773e-02
## [6,] 4.893136e-02 -7.813859e-02
## [7,] 1.148679e-02 -2.273533e-02
## [8,] -2.861022e-02 5.353235e-02
## [9,] -6.177736e-02 8.053437e-02
## [10,] -7.976901e-02 3.324322e-02</code></pre>
## [1,] -2.169611e-05 7.819699e-05
## [2,] 3.884146e-02 6.928805e-02
## [3,] 6.831018e-02 7.508661e-02
## [4,] 8.137611e-02 1.246559e-02
## [5,] 7.445530e-02 -6.122070e-02
## [6,] 4.921439e-02 -7.786260e-02
## [7,] 1.169291e-02 -2.269241e-02
## [8,] -2.876378e-02 5.345657e-02
## [9,] -6.195369e-02 8.026104e-02
## [10,] -7.977416e-02 3.286764e-02</code></pre>
<p>As you can see the loadings are still the same but the probabilistic algorithm is about 15 times faster.</p>

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