<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Oh, never mind my previous email, because while the components should be the same, the projection of the data points onto those components would still be affected by centering vs non-centering I guess.<div class=""><br class=""></div><div class="">Best,</div><div class="">Sebastian<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Oct 16, 2017, at 3:25 PM, Sebastian Raschka <<a href="mailto:se.raschka@gmail.com" class="">se.raschka@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html; charset=us-ascii" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hi,<div class=""><br class=""></div><div class="">if you compute the principal components (i.e., eigendecomposition) from the covariance matrix, it shouldn't matter whether the data is centered or not, since the covariance matrix is computed as </div><div class=""><br class=""></div><div class="">CovMat = \fact{1}{n} \sum_{i=1}^{n} (x_n - \bar{x}) (x_n - \bar{x})^T</div><div class=""><br class=""></div><div class="">where \bar{x} = vector of feature means</div><div class=""><br class=""></div><div class="">So, if you center the data prior to computing the covariance matrix, \bar{x} is simply 0.</div><div class=""><br class=""></div><div class="">Best,</div><div class="">Sebastian<br class=""><div class=""><br class=""><blockquote type="cite" class=""><div class="">On Oct 16, 2017, at 2:27 PM, Ismael Lemhadri <<a href="mailto:lemhadri@stanford.edu" class="">lemhadri@stanford.edu</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">@Andreas Muller: </div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">My references do not assume centering, e.g. <a href="http://ufldl.stanford.edu/wiki/index.php/PCA" class="">http://ufldl.stanford.edu/wiki/index.php/PCA</a></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">any reference?</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br class=""></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br class=""></div><div class="gmail_extra"><br class=""><div class="gmail_quote">On Mon, Oct 16, 2017 at 10:20 AM, <span dir="ltr" class=""><<a href="mailto:scikit-learn-request@python.org" target="_blank" class="">scikit-learn-request@python.org</a>></span> wrote:<br class=""><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Send scikit-learn mailing list submissions to<br class="">
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1. Re: unclear help file for sklearn.decomposition.pca<br class="">
(Andreas Mueller)<br class="">
<br class="">
<br class="">
------------------------------<wbr class="">------------------------------<wbr class="">----------<br class="">
<br class="">
Message: 1<br class="">
Date: Mon, 16 Oct 2017 13:19:57 -0400<br class="">
From: Andreas Mueller <<a href="mailto:t3kcit@gmail.com" class="">t3kcit@gmail.com</a>><br class="">
To: <a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a><br class="">
Subject: Re: [scikit-learn] unclear help file for<br class="">
sklearn.decomposition.pca<br class="">
Message-ID: <<a href="mailto:04fc445c-d8f3-a3a9-4ab2-0535826a2d03@gmail.com" class="">04fc445c-d8f3-a3a9-4ab2-<wbr class="">0535826a2d03@gmail.com</a>><br class="">
Content-Type: text/plain; charset="utf-8"; Format="flowed"<br class="">
<br class="">
The definition of PCA has a centering step, but no scaling step.<br class="">
<br class="">
On 10/16/2017 11:16 AM, Ismael Lemhadri wrote:<br class="">
> Dear Roman,<br class="">
> My concern is actually not about not mentioning the scaling but about<br class="">
> not mentioning the centering.<br class="">
> That is, the sklearn PCA removes the mean but it does not mention it<br class="">
> in the help file.<br class="">
> This was quite messy for me to debug as I expected it to either: 1/<br class="">
> center and scale simultaneously or / not scale and not center either.<br class="">
> It would be beneficial to explicit the behavior in the help file in my<br class="">
> opinion.<br class="">
> Ismael<br class="">
><br class="">
> On Mon, Oct 16, 2017 at 8:02 AM, <<a href="mailto:scikit-learn-request@python.org" class="">scikit-learn-request@python.<wbr class="">org</a><br class="">
> <mailto:<a href="mailto:scikit-learn-request@python.org" class="">scikit-learn-request@<wbr class="">python.org</a>>> wrote:<br class="">
><br class="">
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> than "Re: Contents of scikit-learn digest..."<br class="">
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> Today's Topics:<br class="">
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> ? ?1. unclear help file for sklearn.decomposition.pca (Ismael<br class="">
> Lemhadri)<br class="">
> ? ?2. Re: unclear help file for sklearn.decomposition.pca<br class="">
> ? ? ? (Roman Yurchak)<br class="">
> ? ?3. Question about LDA's coef_ attribute (Serafeim Loukas)<br class="">
> ? ?4. Re: Question about LDA's coef_ attribute (Alexandre Gramfort)<br class="">
> ? ?5. Re: Question about LDA's coef_ attribute (Serafeim Loukas)<br class="">
><br class="">
><br class="">
> ------------------------------<wbr class="">------------------------------<wbr class="">----------<br class="">
><br class="">
> Message: 1<br class="">
> Date: Sun, 15 Oct 2017 18:42:56 -0700<br class="">
> From: Ismael Lemhadri <<a href="mailto:lemhadri@stanford.edu" class="">lemhadri@stanford.edu</a><br class="">
> <mailto:<a href="mailto:lemhadri@stanford.edu" class="">lemhadri@stanford.edu</a>><wbr class="">><br class="">
> To: <a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>><br class="">
> Subject: [scikit-learn] unclear help file for<br class="">
> ? ? ? ? sklearn.decomposition.pca<br class="">
> Message-ID:<br class="">
> ? ? ? ?<br class="">
> <CANpSPFTgv+<wbr class="">Oz7f97dandmrBBayqf_o9w=<a href="mailto:18oKHCFN0u5DNzj%2Bg@mail.gmail.com" class="">18oKHCF<wbr class="">N0u5DNzj+g@mail.gmail.com</a><br class="">
> <mailto:<a href="mailto:18oKHCFN0u5DNzj%252Bg@mail.gmail.com" class="">18oKHCFN0u5DNzj%2Bg@<wbr class="">mail.gmail.com</a>>><br class="">
> Content-Type: text/plain; charset="utf-8"<br class="">
><br class="">
> Dear all,<br class="">
> The help file for the PCA class is unclear about the preprocessing<br class="">
> performed to the data.<br class="">
> You can check on line 410 here:<br class="">
> <a href="https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/" rel="noreferrer" target="_blank" class="">https://github.com/scikit-<wbr class="">learn/scikit-learn/blob/<wbr class="">ef5cb84a/sklearn/</a><br class="">
> decomposition/pca.py#L410<br class="">
> <<a href="https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/%0Adecomposition/pca.py#L410" rel="noreferrer" target="_blank" class="">https://github.com/scikit-<wbr class="">learn/scikit-learn/blob/<wbr class="">ef5cb84a/sklearn/%<wbr class="">0Adecomposition/pca.py#L410</a>><br class="">
> that the matrix is centered but NOT scaled, before performing the<br class="">
> singular<br class="">
> value decomposition.<br class="">
> However, the help files do not make any mention of it.<br class="">
> This is unclear for someone who, like me, just wanted to compare<br class="">
> that the<br class="">
> PCA and np.linalg.svd give the same results. In academic settings,<br class="">
> students<br class="">
> are often asked to compare different methods and to check that<br class="">
> they yield<br class="">
> the same results. I expect that many students have confronted this<br class="">
> problem<br class="">
> before...<br class="">
> Best,<br class="">
> Ismael Lemhadri<br class="">
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><br class="">
> ------------------------------<br class="">
><br class="">
> Message: 2<br class="">
> Date: Mon, 16 Oct 2017 15:16:45 +0200<br class="">
> From: Roman Yurchak <<a href="mailto:rth.yurchak@gmail.com" class="">rth.yurchak@gmail.com</a><br class="">
> <mailto:<a href="mailto:rth.yurchak@gmail.com" class="">rth.yurchak@gmail.com</a>><wbr class="">><br class="">
> To: Scikit-learn mailing list <<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a><br class="">
> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>>><br class="">
> Subject: Re: [scikit-learn] unclear help file for<br class="">
> ? ? ? ? sklearn.decomposition.pca<br class="">
> Message-ID: <<a href="mailto:b2abdcfd-4736-929e-6304-b93832932043@gmail.com" class="">b2abdcfd-4736-929e-6304-<wbr class="">b93832932043@gmail.com</a><br class="">
> <mailto:<a href="mailto:b2abdcfd-4736-929e-6304-b93832932043@gmail.com" class="">b2abdcfd-4736-929e-<wbr class="">6304-b93832932043@gmail.com</a>>><br class="">
> Content-Type: text/plain; charset=utf-8; format=flowed<br class="">
><br class="">
> Ismael,<br class="">
><br class="">
> as far as I saw the sklearn.decomposition.PCA doesn't mention<br class="">
> scaling at<br class="">
> all (except for the whiten parameter which is post-transformation<br class="">
> scaling).<br class="">
><br class="">
> So since it doesn't mention it, it makes sense that it doesn't do any<br class="">
> scaling of the input. Same as np.linalg.svd.<br class="">
><br class="">
> You can verify that PCA and np.linalg.svd yield the same results, with<br class="">
><br class="">
> ```<br class="">
> ?>>> import numpy as np<br class="">
> ?>>> from sklearn.decomposition import PCA<br class="">
> ?>>> import numpy.linalg<br class="">
> ?>>> X = np.random.RandomState(42).<wbr class="">rand(10, 4)<br class="">
> ?>>> n_components = 2<br class="">
> ?>>> PCA(n_components, svd_solver='full').fit_<wbr class="">transform(X)<br class="">
> ```<br class="">
><br class="">
> and<br class="">
><br class="">
> ```<br class="">
> ?>>> U, s, V = np.linalg.svd(X - X.mean(axis=0), full_matrices=False)<br class="">
> ?>>> (X - X.mean(axis=0)).dot(V[:n_<wbr class="">components].T)<br class="">
> ```<br class="">
><br class="">
> --<br class="">
> Roman<br class="">
><br class="">
> On 16/10/17 03:42, Ismael Lemhadri wrote:<br class="">
> > Dear all,<br class="">
> > The help file for the PCA class is unclear about the preprocessing<br class="">
> > performed to the data.<br class="">
> > You can check on line 410 here:<br class="">
> ><br class="">
> <a href="https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410" rel="noreferrer" target="_blank" class="">https://github.com/scikit-<wbr class="">learn/scikit-learn/blob/<wbr class="">ef5cb84a/sklearn/<wbr class="">decomposition/pca.py#L410</a><br class="">
> <<a href="https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410" rel="noreferrer" target="_blank" class="">https://github.com/scikit-<wbr class="">learn/scikit-learn/blob/<wbr class="">ef5cb84a/sklearn/<wbr class="">decomposition/pca.py#L410</a>><br class="">
> ><br class="">
> <<a href="https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410" rel="noreferrer" target="_blank" class="">https://github.com/scikit-<wbr class="">learn/scikit-learn/blob/<wbr class="">ef5cb84a/sklearn/<wbr class="">decomposition/pca.py#L410</a><br class="">
> <<a href="https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410" rel="noreferrer" target="_blank" class="">https://github.com/scikit-<wbr class="">learn/scikit-learn/blob/<wbr class="">ef5cb84a/sklearn/<wbr class="">decomposition/pca.py#L410</a>>><br class="">
> > that the matrix is centered but NOT scaled, before performing the<br class="">
> > singular value decomposition.<br class="">
> > However, the help files do not make any mention of it.<br class="">
> > This is unclear for someone who, like me, just wanted to compare<br class="">
> that<br class="">
> > the PCA and np.linalg.svd give the same results. In academic<br class="">
> settings,<br class="">
> > students are often asked to compare different methods and to<br class="">
> check that<br class="">
> > they yield the same results. I expect that many students have<br class="">
> confronted<br class="">
> > this problem before...<br class="">
> > Best,<br class="">
> > Ismael Lemhadri<br class="">
> ><br class="">
> ><br class="">
> > ______________________________<wbr class="">_________________<br class="">
> > scikit-learn mailing list<br class="">
> > <a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>><br class="">
> > <a href="https://mail.python.org/mailman/listinfo/scikit-learn" rel="noreferrer" target="_blank" class="">https://mail.python.org/<wbr class="">mailman/listinfo/scikit-learn</a><br class="">
> <<a href="https://mail.python.org/mailman/listinfo/scikit-learn" rel="noreferrer" target="_blank" class="">https://mail.python.org/<wbr class="">mailman/listinfo/scikit-learn</a>><br class="">
> ><br class="">
><br class="">
><br class="">
><br class="">
> ------------------------------<br class="">
><br class="">
> Message: 3<br class="">
> Date: Mon, 16 Oct 2017 15:27:48 +0200<br class="">
> From: Serafeim Loukas <<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a> <mailto:<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a>>><br class="">
> To: <a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>><br class="">
> Subject: [scikit-learn] Question about LDA's coef_ attribute<br class="">
> Message-ID: <<a href="mailto:58C6D0DA-9DE5-4EF5-97C1-48159831F5A9@gmail.com" class="">58C6D0DA-9DE5-4EF5-97C1-<wbr class="">48159831F5A9@gmail.com</a><br class="">
> <mailto:<a href="mailto:58C6D0DA-9DE5-4EF5-97C1-48159831F5A9@gmail.com" class="">58C6D0DA-9DE5-4EF5-<wbr class="">97C1-48159831F5A9@gmail.com</a>>><br class="">
> Content-Type: text/plain; charset="us-ascii"<br class="">
><br class="">
> Dear Scikit-learn community,<br class="">
><br class="">
> Since the documentation of the LDA<br class="">
> (<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a><br class="">
> <<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a>><br class="">
> <<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a><br class="">
> <<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a>>>)<br class="">
> is not so clear, I would like to ask if the lda.coef_ attribute<br class="">
> stores the eigenvectors from the SVD decomposition.<br class="">
><br class="">
> Thank you in advance,<br class="">
> Serafeim<br class="">
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><br class="">
> ------------------------------<br class="">
><br class="">
> Message: 4<br class="">
> Date: Mon, 16 Oct 2017 16:57:52 +0200<br class="">
> From: Alexandre Gramfort <<a href="mailto:alexandre.gramfort@inria.fr" class="">alexandre.gramfort@inria.fr</a><br class="">
> <mailto:<a href="mailto:alexandre.gramfort@inria.fr" class="">alexandre.gramfort@<wbr class="">inria.fr</a>>><br class="">
> To: Scikit-learn mailing list <<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a><br class="">
> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>>><br class="">
> Subject: Re: [scikit-learn] Question about LDA's coef_ attribute<br class="">
> Message-ID:<br class="">
> ? ? ? ?<br class="">
> <<a href="mailto:CADeotZricOQhuHJMmW2Z14cqffEQyndYoxn-OgKAvTMQ7V0Y2g@mail.gmail.com" class="">CADeotZricOQhuHJMmW2Z14cqffEQ<wbr class="">yndYoxn-OgKAvTMQ7V0Y2g@mail.<wbr class="">gmail.com</a><br class="">
> <mailto:<a href="mailto:CADeotZricOQhuHJMmW2Z14cqffEQyndYoxn-OgKAvTMQ7V0Y2g@mail.gmail.com" class="">CADeotZricOQhuHJMmW2Z1<wbr class="">4cqffEQyndYoxn-OgKAvTMQ7V0Y2g@<wbr class="">mail.gmail.com</a>>><br class="">
> Content-Type: text/plain; charset="UTF-8"<br class="">
><br class="">
> no it stores the direction of the decision function to match the<br class="">
> API of<br class="">
> linear models.<br class="">
><br class="">
> HTH<br class="">
> Alex<br class="">
><br class="">
> On Mon, Oct 16, 2017 at 3:27 PM, Serafeim Loukas<br class="">
> <<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a> <mailto:<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a>>> wrote:<br class="">
> > Dear Scikit-learn community,<br class="">
> ><br class="">
> > Since the documentation of the LDA<br class="">
> ><br class="">
> (<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a><br class="">
> <<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a>>)<br class="">
> > is not so clear, I would like to ask if the lda.coef_ attribute<br class="">
> stores the<br class="">
> > eigenvectors from the SVD decomposition.<br class="">
> ><br class="">
> > Thank you in advance,<br class="">
> > Serafeim<br class="">
> ><br class="">
> > ______________________________<wbr class="">_________________<br class="">
> > scikit-learn mailing list<br class="">
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> ><br class="">
><br class="">
><br class="">
> ------------------------------<br class="">
><br class="">
> Message: 5<br class="">
> Date: Mon, 16 Oct 2017 17:02:46 +0200<br class="">
> From: Serafeim Loukas <<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a> <mailto:<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a>>><br class="">
> To: Scikit-learn mailing list <<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a><br class="">
> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>>><br class="">
> Subject: Re: [scikit-learn] Question about LDA's coef_ attribute<br class="">
> Message-ID: <<a href="mailto:413210D2-56AE-41A4-873F-D171BB36539D@gmail.com" class="">413210D2-56AE-41A4-873F-<wbr class="">D171BB36539D@gmail.com</a><br class="">
> <mailto:<a href="mailto:413210D2-56AE-41A4-873F-D171BB36539D@gmail.com" class="">413210D2-56AE-41A4-<wbr class="">873F-D171BB36539D@gmail.com</a>>><br class="">
> Content-Type: text/plain; charset="us-ascii"<br class="">
><br class="">
> Dear Alex,<br class="">
><br class="">
> Thank you for the prompt response.<br class="">
><br class="">
> Are the eigenvectors stored in some variable ?<br class="">
> Does the lda.scalings_ attribute contain the eigenvectors ?<br class="">
><br class="">
> Best,<br class="">
> Serafeim<br class="">
><br class="">
> > On 16 Oct 2017, at 16:57, Alexandre Gramfort<br class="">
> <<a href="mailto:alexandre.gramfort@inria.fr" class="">alexandre.gramfort@inria.fr</a> <mailto:<a href="mailto:alexandre.gramfort@inria.fr" class="">alexandre.gramfort@<wbr class="">inria.fr</a>>><br class="">
> wrote:<br class="">
> ><br class="">
> > no it stores the direction of the decision function to match the<br class="">
> API of<br class="">
> > linear models.<br class="">
> ><br class="">
> > HTH<br class="">
> > Alex<br class="">
> ><br class="">
> > On Mon, Oct 16, 2017 at 3:27 PM, Serafeim Loukas<br class="">
> <<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a> <mailto:<a href="mailto:seralouk@gmail.com" class="">seralouk@gmail.com</a>>> wrote:<br class="">
> >> Dear Scikit-learn community,<br class="">
> >><br class="">
> >> Since the documentation of the LDA<br class="">
> >><br class="">
> (<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a><br class="">
> <<a href="http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html" rel="noreferrer" target="_blank" class="">http://scikit-learn.org/<wbr class="">stable/modules/generated/<wbr class="">sklearn.discriminant_analysis.<wbr class="">LinearDiscriminantAnalysis.<wbr class="">html</a>>)<br class="">
> >> is not so clear, I would like to ask if the lda.coef_ attribute<br class="">
> stores the<br class="">
> >> eigenvectors from the SVD decomposition.<br class="">
> >><br class="">
> >> Thank you in advance,<br class="">
> >> Serafeim<br class="">
> >><br class="">
> >> ______________________________<wbr class="">_________________<br class="">
> >> scikit-learn mailing list<br class="">
> >> <a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.org</a> <mailto:<a href="mailto:scikit-learn@python.org" class="">scikit-learn@python.<wbr class="">org</a>><br class="">
> >> <a href="https://mail.python.org/mailman/listinfo/scikit-learn" rel="noreferrer" target="_blank" class="">https://mail.python.org/<wbr class="">mailman/listinfo/scikit-learn</a><br class="">
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> >><br class="">
> > ______________________________<wbr class="">_________________<br class="">
> > scikit-learn mailing list<br class="">
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