svn commit: r1576421 - /mahout/site/mahout_cms/trunk/content/users/dim-reduction/ssvd.mdtext

[dl...@apache.org]

Author: dlyubimov
Date: Tue Mar 11 16:50:52 2014
New Revision: 1576421

URL: http://svn.apache.org/r1576421
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=1576421&r1=1576420&r2=1576421&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 Tue Mar 11 16:50:52 2014
@@ -98,8 +98,8 @@ this procedure computes an `\(m\times\le
 SVD `\(\mathbf{A\approx U}\boldsymbol{\Sigma}\mathbf{V}^{\top}\)`:
 
   1. Create seed for random `\(n\times\left(k+p\right)\)`
-  matrix `\(\boldsymbol{\Omega}\)` The seed defines matrix `\(\mathbf{\Omega}\)`
-  using Gaussian unit vectors per one of suggestions in [Martinsson].
+  matrix `\(\boldsymbol{\Omega}\)`. The seed defines matrix `\(\mathbf{\Omega}\)`
+  using Gaussian unit vectors per one of suggestions in [Halko, Martinsson, Tropp].
 
   2. `\(\mathbf{Y=A\boldsymbol{\Omega}},\,\mathbf{Y}\in\mathbb{R}^{m\times\left(k+p\right)}\)`
  
@@ -130,6 +130,8 @@ SVD `\(\mathbf{A\approx U}\boldsymbol{\S
 
   9. If needed, compute `\(\mathbf{V}=\mathbf{B}_{q}^{\top}\hat{\mathbf{U}}\boldsymbol{\Sigma}^{-1}\)`.
 Another way is `\(\mathbf{V}=\mathbf{A}^{\top}\mathbf{U}\boldsymbol{\Sigma}^{-1}\)`.
+
+[Halko, Martinsson, Tropp]: http://arxiv.org/abs/0909.4061
  
 
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