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From Lance Norskog <goks...@gmail.com>
Subject Re: Relative measure of rank
Date Mon, 13 Dec 2010 04:33:59 GMT
Should be "scalar or vector".  I'm interested in the loss of precision
by dimensional reduction algorithms: matrix difference is only defined
for same-size matrices. So, there is no real absolute measure, just
relative measures that are not very useful except for certain use
cases.

On Sun, Dec 12, 2010 at 7:21 PM, Ted Dunning <ted.dunning@gmail.com> wrote:
> What do you mean by rank of a matrix?  The normal definition is the number
> of non-zero singular values.  This
> doesn't sound like what you mean.
>
> What do you mean by loss of information?  If you mean how do you compare an
> approximation of a matrix
> versus the original, yes there are ways of doing that, not all very useful.
>  Norm of the difference is one example
> that leads to least squares formulations.
>
> Also, is there something missing from the sentence with "scalar of vector"
> in it?
>
> On Sun, Dec 12, 2010 at 6:04 PM, Lance Norskog <goksron@gmail.com> wrote:
>
>> Given a matrix reduction algorithm, how do you measure the loss of
>> information perpetrated by the algorithm on the poor defenseless input
>> matrix?
>> Are there algorithms to compare two matrices and get a relative rank value?
>>
>> Is there a scalar of vector that describes the rank of a matrix? Then
>> you could just compare the two rank values.
>>
>> Is there a probabilistic approach to the problem?
>>
>> --
>> Lance Norskog
>> goksron@gmail.com
>>
>



-- 
Lance Norskog
goksron@gmail.com

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