Reading further... Yep. that's exactly how it is done there in
distributed QR solver. At least on top of it.
On Thu, Feb 23, 2012 at 4:54 PM, Dmitriy Lyubimov <dlie...@gmail.com> wrote:
> Wow. Cantor patterns for Givens rotations. I wondered if it already
> had a name or somebody already figured to do something similar. It
> looks like you really got into that level of details there. That's
> extremely cool, sir !
>
> On Thu, Feb 23, 2012 at 4:45 PM, Dmitriy Lyubimov <dlie...@gmail.com> wrote:
>> Thank you, Nathan.
>>
>> On Wed, Feb 22, 2012 at 7:01 PM, Nathan Halko <nat...@spotinfluence.com>
>> wrote:
>>> Hi Dmitriy,
>>>
>>> Just a few comments:
>>>
>>> --the computed factors are approximate A \approx U\SigmaV^{T}
>>
>> Thanks, agreed.
>>
>>>
>>> -- the projection steps seemed transposed to me but they are consistent
>>> throughout ie.
>>> (2) \tilde{u} = \tilde{c}_{r} V \Sigma^{-1}
>>
>> Yes this is probably an earlier error, but in section 3 fold in
>> expressions I beleive should be correct. I assume the convention is
>> that all vectors in equations have columnar orientation (i.e. x'x is
>> inner product, xx' is always outer product). I will check it
>>
>>>
>>> p. 3: transpose \xi to emphasize row vector
>>>
>>> - 'mean of all rows' is a bit misleading, \xi entries are the mean of each
>>> column (column-wise mean as you state below)
>>>
>>
>> Yeah this keeps coming up. means of rows is the same as column mean.
>> Column mean seems to sound more familiar to people, but mean of rows
>> seems to be more visual: if we have a bunch of data points in multiple
>> dimensions and compute their 'center' (mean) then we say "center of
>> points', or applying to pca situation it converts to 'mean of rows'.
>> But i think concensus is growing that we should always opt out for
>> 'column mean' or at least not mix the two to prevent confusion.
>>
>>
>>> - dimention -> dimension
>>>
>>> I haven't code dived into the new pca code to be familiar with it so the
>>> above comments are just picky notational stuff. I did however, do some
>>> extensive analysis on the standard decomposition part (as of 0.6 SNAPSHOT)
>>> which can be found here
>>
>>
>> Yeah i meant validation of PCA approach. There seems to be somewhat
>> different ways to do it. Some people run eigendecomposition on a
>> covariance matrix which i guess would be adjusted for 1/n. which
>> should be technically equivalent to running svd and then adjusting
>> singular values for n^-0.5 but since nobody really cares about
>> singular values after PCA is done, it seems to be moot. Also it
>> doesn't seem to affect the transformational equations in any way.
>>
>> I was also not sure if i could safely label U rows as original
>> datapoints converted into PCA space (is there is such a thing as PCA
>> space anyway? I saw this concept in some texts i think but i now not
>> sure what was meant by it back there).
>>
>>>
>>> http://amath.colorado.edu/faculty/martinss/Pubs/2012_halko_dissertation.pdf
>>> (starting page 139)
>>
>> This is all cool stuff. I will read it as soon as i get a spare time
>> window. Great!
>>
>> once again, thank you for doing this.
>>
>> -d
