trouble with Wt argument of matplotlib.mlab.PCA

Community matplotlib-users
1

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?
thanks,
Justin

2

Justin, could you post a self-contained script that demonstrates the
issue? Where does this PCA function come from?

In [1]: from pylab import *

In [2]: PCA

···

On Mon, Jun 11, 2012 at 11:03 PM, Justin R <justinbrowe@...287...> 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?
thanks,
Justin

---------------------------------------------------------------------------
NameError Traceback (most recent call last)
C:\Users\phobson\<ipython-input-2-dcf6991f51c0> in <module>()
----> 1 PCA

NameError: name 'PCA' is not defined

-paul

3

2012/6/12 Paul Hobson <pmhobson@...287...>:

···

On Mon, Jun 11, 2012 at 11:03 PM, Justin R <justinbrowe@...287...> wrote:
Justin, could you post a self-contained script that demonstrates the
issue? Where does this PCA function come from?

It comes from matplotlib.mlab. Just add these imports before the OP's code:

import numpy as np
from matplotlib.mlab import PCA

But I don't know much about PCA and can't comment on this.

Goyo

4

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 = dat32 + 3np.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?

thanks,

Justin

Justin, could you post a self-contained script that demonstrates the

issue? Where does this PCA function come from?

In [1]: from pylab import *

In [2]: PCA

NameError Traceback (most recent call last)

C:\Users\phobson<ipython-input-2-dcf6991f51c0> in ()

----> 1 PCA

NameError: name ‘PCA’ is not defined

Paul,

In case you never got an answer to this: PCA is in the mlab submodule, so if you do “from pylab import *”, you would use mlab.PCA. (At least that’s the case in matplotlib 1.1.0).

Warren

···

On Tue, Jun 12, 2012 at 11:59 AM, Paul Hobson <pmhobson@…287…> wrote:

On Mon, Jun 11, 2012 at 11:03 PM, Justin R <justinbrowe@…287…> wrote:

-paul

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5

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 Tue, Jun 12, 2012 at 1:03 AM, Justin R <justinbrowe@...287...> 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?