plot PCA of transpose of matrix

[vivekbhr]

plotPCA issue (not projecting the samples properly, #477 ) is fixed in R by using a transpose of matrix (scaling/centering is not required). But matplotlib.mlab.PCA doesn't accept a transposed matrix. We need to fix this issue.

[dpryan79]

@vivekbhr Do you still have the numpy file for this?

[vivekbhr]

@dpryan79 yes.. can share with you ..

[dpryan79]

It looks like the following works (m is a numpy matrix with nrows > ncols):

U, s, V = np.linalg.svd(m.T, full_matrices=False)
return np.dot(m.T, V.T)

That's among what prcomp() is doing internally from the best I can tell.

[dpryan79]

I'm not sure SVD is really returning equivalent results to what R is doing in this case. I tried the above code on a play dataset and got reasonable results, but I only got nonsense on real data. This may well turn into a "can't implement without rewriting parts of numpy". I'll remove this from the 2.5 milestone, since I don't think it'll happen for that.

[fidelram]

for a different PCA implementation we will need to use sklearn or statsmodels (or find out how they do the PCA).

…

On Wed, Mar 29, 2017 at 8:42 AM, Devon Ryan ***@***.***> wrote: I'm not sure SVD is really returning equivalent results to what R is doing in this case. I tried the above code on a play dataset and got reasonable results, but I only got nonsense on real data. This may well turn into a "can't implement without rewriting parts of numpy". I'll remove this from the 2.5 milestone, since I don't think it'll happen for that. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#496 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AEu_1UDHCZAsmDvf1NNpfTJvsXiusEBXks5rqf1QgaJpZM4MoFs0> .

-- Fidel Ramirez

[dpryan79]

I tried sklearn briefly but didn't get much better results.

[dpryan79]

Here's the python code that seems to work correctly (m is a matrix with nrows > ncols):

m2 = (m.T - np.mean(m, axis=1))
U, s, V = np.linalg.svd(m2, full_matrices=False, compute_uv=True)
V = V.T
PCs = np.dot(m2, V)

Each column of PCs is a principal component, with rows as samples. This matches with what R is doing.

[dpryan79]

@vivekbhr There's now a betterPCA branch, which adds the --transpose, --ntop, and --PCs options. --transpose will produce the PCA on the transposed matrix. As in R, the projection of the samples on the PCs is then plotted rather than the weights/loadings. --ntop specifies how many of the top N most variable rows to use for the PCA (again, exactly as in R). --PCs specifies which components to plot. The default is 1 2, but you can specify whichever components you want. This should then produce exactly the same output as you'd get with prcomp(foo, scale=T, center=T) in R.

[dpryan79]

I seem to now be getting the same results as prcomp, which makes me happy. Even the scaling that matplotlib was doing was suboptimal (it wasn't using Bessel's correction). This is all implemented in the develop branch now and will be included in the 2.6 release.