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
