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Posted to commits@mahout.apache.org by dl...@apache.org on 2014/03/10 06:08:34 UTC
svn commit: r1575826 -
/mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext
Author: dlyubimov
Date: Mon Mar 10 05:08:34 2014
New Revision: 1575826
URL: http://svn.apache.org/r1575826
Log:
CMS commit to mahout by dlyubimov
Modified:
mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext
Modified: mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext
URL: http://svn.apache.org/viewvc/mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext?rev=1575826&r1=1575825&r2=1575826&view=diff
==============================================================================
--- mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext (original)
+++ mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext Mon Mar 10 05:08:34 2014
@@ -89,13 +89,13 @@ Note: numerical stability of R algorithm
#### Modified SSVD Algorithm. ####
-
-Given an $m\times n$
- matrix A, a target rank $k\in\mathbb{N}_{1}$
- , an oversampling parameter $p\in\mathbb{N}_{1}$
- , and the number of additional power iterations $q\in\mathbb{N}_{0}$
- , this procedure computes an $m\times\left(k+p\right)$
- SVD $\mathbf{A\approx U}\boldsymbol{\Sigma}\mathbf{V}^{\top}$
+<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-45" 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-46" 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-47" 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-48" 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-49" 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-50" type="math/tex">\mathbf{A\approx U}\boldsymbol{\Sigma}\mathbf{V}^{\top}</script></p>
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