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From build...@apache.org
Subject svn commit: r900862 - in /websites/staging/mahout/trunk/content: ./ users/dim-reduction/ssvd.html
Date Mon, 10 Mar 2014 07:35:14 GMT
Author: buildbot
Date: Mon Mar 10 07:35:14 2014
New Revision: 900862

Log:
Staging update by buildbot for mahout

Modified:
    websites/staging/mahout/trunk/content/   (props changed)
    websites/staging/mahout/trunk/content/users/dim-reduction/ssvd.html

Propchange: websites/staging/mahout/trunk/content/
------------------------------------------------------------------------------
--- cms:source-revision (original)
+++ cms:source-revision Mon Mar 10 07:35:14 2014
@@ -1 +1 @@
-1575853
+1575855

Modified: websites/staging/mahout/trunk/content/users/dim-reduction/ssvd.html
==============================================================================
--- websites/staging/mahout/trunk/content/users/dim-reduction/ssvd.html (original)
+++ websites/staging/mahout/trunk/content/users/dim-reduction/ssvd.html Mon Mar 10 07:35:14
2014
@@ -255,8 +255,17 @@ x<span class="o">&lt;-</span> usim <span
 
 <p>and try to compare ssvd.svd(x) and stock svd(x) performance for the same rank k,
notice the difference in the running time. Also play with power iterations (qIter) and compare
accuracies of standard svd and SSVD.</p>
 <p>Note: numerical stability of R algorithms may differ from that of Mahout's distributed
version. We haven't studied accuracy of the R simulation. For study of accuracy of Mahout's
version, please refer to Nathan's dissertation as referenced above.</p>
-<p>test <code>inline code</code> here.</p>
-<p>Given an <code>\(m\times n\)</code> kllkdklsdf</p>
+<p>Given an <code>\(m\times n\)</code>
+matrix <code>\(\mathbb{A}\)</code>, a target rank <code>\(k\in\mathbb{N}_{1}\)</code>
+, an oversampling parameter <code>\(p\in\mathbb{N}_{1}\)</code>, 
+and the number of additional power iterations <code>\(q\in\mathbb{N}_{0}\)</code>,

+this procedure computes an <code>\(m\times\left(k+p\right)\)</code>
+SVD <code>\(\mathbf{A\approx U}\boldsymbol{\Sigma}\mathbf{V}^{\top}\)</code>:</p>
+<ol>
+<li>Create seed for random <code>\(n\times\left(k+p\right)\)</code>
+  matrix <code>\(\boldsymbol{\Omega}\)</code> The seed defines matrix <code>\(\mathbf{\Omega}\)</code>
+  using Gaussian unit vectors per one of suggestions in [Martinsson].</li>
+</ol>
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