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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...Just to throw another bit. Just like Ted was saying. If you take the largest singular value over the smallest singular value, you get your condition number. If it turns out to be 10^16, then...
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Author: Koobas,
2013-04-04, 17:10
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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...For what it's worth, here's what I remember from my Numerical Analysis course. The thing we were taught to use to figure out whether the matrix is ill conditioned is the condition numb...
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Author: Dan Filimon,
2013-04-04, 16:21
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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...I have a feeling, it is a problem with the ALS algorithm. Unlike in SVD, you're not getting orthogonal vectors. So, X and Y matrices can be rank-deficient. Then, multiplying X (or Y) by its ...
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Author: Koobas,
2013-04-04, 15:42
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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...I think that's what I'm saying, yes. Small rows X shouldn't become large rows of A -- and similarly small changes in X shouldn't mean large changes in A. Not quite the same thing but both ar...
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Author: Sean Owen,
2013-04-04, 14:26
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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...On Thu, Apr 4, 2013 at 9:36 AM, Sean Owen wrote: So, the problem is that the kxk matrix is ill-conditioned, or is there more to it? ...
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Author: Koobas,
2013-04-04, 14:19
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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...On Thu, Apr 4, 2013 at 9:13 AM, Ted Dunning wrote: Wouldn't it be better to use Householder? ...
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Author: Koobas,
2013-04-04, 14:16
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Re: Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...Yeah I've got the pivoting part down -- I think. The problem is that I can't seem to identify the problem by simple thresholding. For example, a diagonal like "10 9 8 0.0001 0.0000001" obvio...
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Author: Sean Owen,
2013-04-04, 13:36
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Detecting rank-deficiency, or worse, via QR decomposition - Mahout - [mail # user]
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...This is more of a linear algebra question, but I thought it worth posing to the group -- As part of a process like ALS, you solve a system like A = X * Y' for X or for Y, given the oth...
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Author: Sean Owen,
2013-04-04, 10:41
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Re: need review for stochastic matrix decomposition doc - Mahout - [mail # dev]
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...The qr step that I am talking about is, indeed, QR decomposition and would typically be implemented with a sequential local implementation of Gram-Schmidt. The win in the outline that I...
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... gave was that I was proposing decomposing independent blocks of the A Omega product rather than the whole thing at once. This block decomposition *is* parallelizable, but it isn't really a QR...
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| ... decomposition of the entire matrix. It does, however, provide an orthonormal basis of A Omega. Since we don't care about the R part of the decomposition anyway, that seems good enough. (let me know... |
| ... if there is somewhere that I could describe the process better to make clear that I am suggesting decomposition of indepdendent blocks) On Sun, Apr 11, 2010 at 9:55 PM, Dmitriy Lyubimov wrote: ... |
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Author: Ted Dunning,
2010-04-12, 05:54
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need review for stochastic matrix decomposition doc - Mahout - [mail # dev]
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...I am working out the details of a fully scalable MR implementation of the stochastic decomposition and would appreciate some reviews. See https://issues.apache.org/jira/browse/MAHOUT-376...
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Author: Ted Dunning,
2010-04-11, 13:49
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