You are viewing a plain text version of this content. The canonical link for it is here.
Posted to commits@mahout.apache.org by bu...@apache.org on 2014/03/10 07:53:00 UTC
svn commit: r900850 - in /websites/staging/mahout/trunk/content: ./
users/dim-reduction/ssvd.html
Author: buildbot
Date: Mon Mar 10 06:53:00 2014
New Revision: 900850
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 06:53:00 2014
@@ -1 +1 @@
-1575833
+1575844
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 06:53:00 2014
@@ -255,6 +255,15 @@ x<span class="o"><-</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>Modified SSVD Algorithm.</p>
+
+<p>Given an <span style="display: none;" class="MathJax_Preview"></span><span style="font-size: 100%;" class="MathJax_MathML"><math><mi>m</mi><mo stretchy="false">Ã</mo><mi>n</mi></math></span><script id="MathJax-Element-57" type="math/tex">m\times n</script>
+ matrix A, a target rank <span style="display: none;" class="MathJax_Preview"></span><span style="font-size: 100%;" class="MathJax_MathML"><math><mi>k</mi><mo stretchy="false">â</mo><msub><mrow><mi mathvariant="double-struck">N</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span><script id="MathJax-Element-58" type="math/tex">k\in\mathbb{N}_{1}</script>
+ , an oversampling parameter <span style="display: none;" class="MathJax_Preview"></span><span style="font-size: 100%;" class="MathJax_MathML"><math><mi>p</mi><mo stretchy="false">â</mo><msub><mrow><mi mathvariant="double-struck">N</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span><script id="MathJax-Element-59" type="math/tex">p\in\mathbb{N}_{1}</script>
+ , and the number of additional power iterations <span style="display: none;" class="MathJax_Preview"></span><span style="font-size: 100%;" class="MathJax_MathML"><math><mi>q</mi><mo stretchy="false">â</mo><msub><mrow><mi mathvariant="double-struck">N</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><script id="MathJax-Element-60" type="math/tex">q\in\mathbb{N}_{0}</script>
+ , this procedure computes an <span style="display: none;" class="MathJax_Preview"></span><span style="font-size: 100%;" class="MathJax_MathML"><math><mi>m</mi><mo stretchy="false">Ã</mo><mfenced close=")" open="("><mrow><mi>k</mi><mo stretchy="false">+</mo><mi>p</mi></mrow></mfenced></math></span><script id="MathJax-Element-61" type="math/tex">m\times\left(k+p\right)</script>
+ SVD <span style="display: none;" class="MathJax_Preview"></span><span style="font-size: 100%;" class="MathJax_MathML"><math><mrow><mi mathvariant="bold">A</mi><mo stretchy="false">â</mo><mi mathvariant="bold">U</mi></mrow><mi mathvariant="bold">Σ</mi><msup><mrow><mi mathvariant="bold">V</mi></mrow><mrow><mi mathvariant="normal">â¤</mi></mrow></msup></math></span><script id="MathJax-Element-62" type="math/tex">\mathbf{A\approx U}\boldsymbol{\Sigma}\mathbf{V}^{\top}</script>:</p>
+
<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>