matplotlib-users Mailing List for matplotlib

On Tue, Jun 12, 2012 at 1:03 AM, Justin R <jus...@gm...> wrote:
> operating system Windows 7
> matplotlib version : 1.1.0
> obtained from sourceforge
>
> the class seems to generate the same Wt matrix for every input. The
> every element of the weight matrix is either +sqrt(1/2) or -sqrt(1/2).
>
> dat1 = 4*np.random.randn(200,1) + 2
> dat2 = dat1*.25 + 1*np.random.randn(200,1)
> pcaObj1 = PCA(np.hstack((dat1,dat2)))
> print pcaObj1.Wt
>
> dat3 = 2*np.random.randn(200,1) + 2
> dat4 = dat3*2 + 3*np.random.randn(200,1)
> pcaObj2 = PCA(np.hstack((dat1,dat2)))
> print pcaObj2.Wt
>
> The output Y seems to be correct, and the projection function works.
> only the Wt matrix seems to be messed up. Am I using this class
> incorrectly, or could this be a bug?

Hi,


I wouldn't call myself a PCA expert - so don't weight my answer too
heavily - but here is what I think is happening:

Looking at the code, the input data array is centered and scaled to
unit variance in each dimension. The attribute .a of the class is a
copy of the array that is actually sent to the SVD; note the
centering/scaling. I don't have a proof of this, but intuitively I
expect that the PCA axes associated with a 2-dimension centered/scaled
array will always be at 45" angles (e.g., [1,1], [-1,1], etc., which
are normalized to [sqrt(1/2), sqrt(1/2)], etc). I think one way to
describe this is that after centering/scaling there are no degrees of
freedom left if you only started with 2 dimensions. So I don't think
there is a bug, but it is maybe unclear what the PCA class is doing.
If you increase to > 2 dimensions, you can see there is random
fluctuation in Wt:

In [102]: pcaObj = PCA(np.random.randn(200,2))
In [103]: pcaObj.Wt
Out[103]:
array([[-0.70710678, -0.70710678],
       [-0.70710678,  0.70710678]])

In [104]: pcaObj = PCA(np.random.randn(200,3))
In [105]: pcaObj.Wt
Out[105]:
array([[ 0.65456366, -0.24141116, -0.7164266 ],
       [ 0.39843462,  0.91551401,  0.05553329],
       [ 0.64249223, -0.32179924,  0.69544877]])

In [106]: pcaObj = PCA(np.random.randn(200,3))
In [107]: pcaObj.Wt
Out[107]:
array([[-0.29885902, -0.67436982,  0.67521007],
       [-0.95428685,  0.21449891, -0.20815098],
       [-0.00446109, -0.70655189, -0.70764718]])


Hope that helps,
Aronne

On Friday, June 15, 2012, Mark Lawrence wrote:

> Hi all,
>
> I regularly use matplotlib for plotting data relating to my personal
> finances.  At the moment I'm converting Decimals to floats.  Do I still
> have to do this?  If yes, are there any plans to support Decimals?  I've
> tried searching the latest PDF document, my apologies if I've missed
> anything, in which case could I have a pointer please.
>
> --
> Cheers.
>
> Mark Lawrence.
>
>
>
Our support for python decimals falls in the same category as any other
non-float datatypes (ints, datetime, etc.): it might work, but probably not
everywhere and most likely will end up being converted into floats anyway
somewhere in the process.

If you see places where Decimal doesn't work, file a bug request so that we
can try to better generalize our code-base.

Cheers!
Ben Root