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