Thank you all for your feedback. The initial problem I came with wasnt the definition of PCA but what the sklearn method does. In practice I would always make sure the data is both centered and scaled before performing PCA. This is the recommended method because without scaling, the biggest direction could wrongly seem to explain a huge fraction of the variance. So my point was simply to clarify in the help file and the user guide what the PCA class does precisely to leave no unclarity to the reader. Moving forward I have now submitted a pull request on github as initially suggested by Roman on this thread. Best, Ismael
On Mon, 16 Oct 2017 at 11:49 AM, <scikit-learn-requ...@python.org> wrote: > Send scikit-learn mailing list submissions to > scikit-learn@python.org > > To subscribe or unsubscribe via the World Wide Web, visit > https://mail.python.org/mailman/listinfo/scikit-learn > or, via email, send a message with subject or body 'help' to > scikit-learn-requ...@python.org > > You can reach the person managing the list at > scikit-learn-ow...@python.org > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of scikit-learn digest..." > > > Today's Topics: > > 1. Re: 1. Re: unclear help file for sklearn.decomposition.pca > (Andreas Mueller) > 2. Re: 1. Re: unclear help file for sklearn.decomposition.pca > (Oliver Tomic) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Mon, 16 Oct 2017 14:44:51 -0400 > From: Andreas Mueller <t3k...@gmail.com> > To: scikit-learn@python.org > Subject: Re: [scikit-learn] 1. Re: unclear help file for > sklearn.decomposition.pca > Message-ID: <35142868-fce9-6cb3-eba3-015a0b106...@gmail.com> > Content-Type: text/plain; charset="utf-8"; Format="flowed" > > > > On 10/16/2017 02:27 PM, Ismael Lemhadri wrote: > > @Andreas Muller: > > My references do not assume centering, e.g. > > http://ufldl.stanford.edu/wiki/index.php/PCA > > any reference? > > > It kinda does but is not very clear about it: > > This data has already been pre-processed so that each of the > features\textstyle x_1and\textstyle x_2have about the same mean (zero) > and variance. > > > > Wikipedia is much clearer: > Consider a datamatrix > <https://en.wikipedia.org/wiki/Matrix_%28mathematics%29>,*X*, with > column-wise zeroempirical mean > <https://en.wikipedia.org/wiki/Empirical_mean>(the sample mean of each > column has been shifted to zero), where each of the/n/rows represents a > different repetition of the experiment, and each of the/p/columns gives > a particular kind of feature (say, the results from a particular sensor). > https://en.wikipedia.org/wiki/Principal_component_analysis#Details > > I'm a bit surprised to find that ESL says "The SVD of the centered > matrix X is another way of expressing the principal components of the > variables in X", > so they assume scaling? They don't really have a great treatment of PCA, > though. > > Bishop <http://www.springer.com/us/book/9780387310732> and Murphy > <https://mitpress.mit.edu/books/machine-learning-0> are pretty clear > that they subtract the mean (or assume zero mean) but don't standardize. > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/81b3014b/attachment-0001.html > > > > ------------------------------ > > Message: 2 > Date: Mon, 16 Oct 2017 20:48:29 +0200 > From: Oliver Tomic <oliverto...@zoho.com> > To: "Scikit-learn mailing list" <scikit-learn@python.org> > Cc: <scikit-learn@python.org> > Subject: Re: [scikit-learn] 1. Re: unclear help file for > sklearn.decomposition.pca > Message-ID: <15f26840d65.e97b33c25239.3934951873824890...@zoho.com> > Content-Type: text/plain; charset="utf-8" > > Dear Ismael, > > > > PCA should always involve at the least centering, or, if the variables are > to contribute equally, scaling. Here is a reference from the scientific > area named "chemometrics". In Chemometrics PCA used not only for > dimensionality reduction, but also for interpretation of variance by use of > scores, loadings, correlation loadings, etc. > > > > If you scroll down to subsection "Preprocessing" you will find more info > on centering and scaling. > > > http://pubs.rsc.org/en/content/articlehtml/2014/ay/c3ay41907j > > > > best > > Oliver > > > > > ---- On Mon, 16 Oct 2017 20:27:11 +0200 Ismael Lemhadri & > lt;lemha...@stanford.edu> wrote ---- > > > > > @Andreas Muller: > > My references do not assume centering, e.g. > http://ufldl.stanford.edu/wiki/index.php/PCA > > any reference? > > > > > > > > On Mon, Oct 16, 2017 at 10:20 AM, <scikit-learn-requ...@python.org> > wrote: > > Send scikit-learn mailing list submissions to > > scikit-learn@python.org > > > > To subscribe or unsubscribe via the World Wide Web, visit > > https://mail.python.org/mailman/listinfo/scikit-learn > > or, via email, send a message with subject or body 'help' to > > scikit-learn-requ...@python.org > > > > You can reach the person managing the list at > > scikit-learn-ow...@python.org > > > > When replying, please edit your Subject line so it is more specific > > than "Re: Contents of scikit-learn digest..." > > > > > > Today's Topics: > > > > 1. Re: unclear help file for sklearn.decomposition.pca > > (Andreas Mueller) > > > > > > ---------------------------------------------------------------------- > > > > Message: 1 > > Date: Mon, 16 Oct 2017 13:19:57 -0400 > > From: Andreas Mueller <t3k...@gmail.com> > > To: scikit-learn@python.org > > Subject: Re: [scikit-learn] unclear help file for > > sklearn.decomposition.pca > > Message-ID: <04fc445c-d8f3-a3a9-4ab2-0535826a2...@gmail.com> > > Content-Type: text/plain; charset="utf-8"; Format="flowed" > > > > The definition of PCA has a centering step, but no scaling step. > > > > On 10/16/2017 11:16 AM, Ismael Lemhadri wrote: > > > Dear Roman, > > > My concern is actually not about not mentioning the scaling but about > > > not mentioning the centering. > > > That is, the sklearn PCA removes the mean but it does not mention it > > > in the help file. > > > This was quite messy for me to debug as I expected it to either: 1/ > > > center and scale simultaneously or / not scale and not center either. > > > It would be beneficial to explicit the behavior in the help file in > my > > > opinion. > > > Ismael > > > > > > On Mon, Oct 16, 2017 at 8:02 AM, <scikit-learn-requ...@python.org > > > <mailto:scikit-learn-requ...@python.org>> wrote: > > > > > > Send scikit-learn mailing list submissions to > > > scikit-learn@python.org <mailto:scikit-learn@python.org> > > > > > > To subscribe or unsubscribe via the World Wide Web, visit > > > https://mail.python.org/mailman/listinfo/scikit-learn > > > <https://mail.python.org/mailman/listinfo/scikit-learn> > > > or, via email, send a message with subject or body 'help' to > > > scikit-learn-requ...@python.org > > > <mailto:scikit-learn-requ...@python.org> > > > > > > You can reach the person managing the list at > > > scikit-learn-ow...@python.org <mailto: > scikit-learn-ow...@python.org> > > > > > > When replying, please edit your Subject line so it is more > specific > > > than "Re: Contents of scikit-learn digest..." > > > > > > > > > Today's Topics: > > > > > > ? ?1. unclear help file for sklearn.decomposition.pca (Ismael > > > Lemhadri) > > > ? ?2. Re: unclear help file for sklearn.decomposition.pca > > > ? ? ? (Roman Yurchak) > > > ? ?3. Question about LDA's coef_ attribute (Serafeim Loukas) > > > ? ?4. Re: Question about LDA's coef_ attribute (Alexandre > Gramfort) > > > ? ?5. Re: Question about LDA's coef_ attribute (Serafeim Loukas) > > > > > > > > > > ---------------------------------------------------------------------- > > > > > > Message: 1 > > > Date: Sun, 15 Oct 2017 18:42:56 -0700 > > > From: Ismael Lemhadri <lemha...@stanford.edu > > > <mailto:lemha...@stanford.edu>> > > > To: scikit-learn@python.org <mailto:scikit-learn@python.org > > > > > Subject: [scikit-learn] unclear help file for > > > ? ? ? ? sklearn.decomposition.pca > > > Message-ID: > > > ? ? ? ? > > > <CANpSPFTgv+Oz7f97dandmrBBayqf_o9w= > 18okhcfn0u5dnz...@mail.gmail.com > > > <mailto:18okhcfn0u5dnzj%...@mail.gmail.com>> > > > Content-Type: text/plain; charset="utf-8" > > > > > > Dear all, > > > The help file for the PCA class is unclear about the > preprocessing > > > performed to the data. > > > You can check on line 410 here: > > > > https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/ > > > decomposition/pca.py#L410 > > > < > https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/%0Adecomposition/pca.py#L410> > ; > > > that the matrix is centered but NOT scaled, before performing the > > > singular > > > value decomposition. > > > However, the help files do not make any mention of it. > > > This is unclear for someone who, like me, just wanted to compare > > > that the > > > PCA and np.linalg.svd give the same results. In academic > settings, > > > students > > > are often asked to compare different methods and to check that > > > they yield > > > the same results. I expect that many students have confronted > this > > > problem > > > before... > > > Best, > > > Ismael Lemhadri > > > -------------- next part -------------- > > > An HTML attachment was scrubbed... > > > URL: > > > < > http://mail.python.org/pipermail/scikit-learn/attachments/20171015/c465bde7/attachment-0001.html > > > < > http://mail.python.org/pipermail/scikit-learn/attachments/20171015/c465bde7/attachment-0001.html>> > ; > > > > > > ------------------------------ > > > > > > Message: 2 > > > Date: Mon, 16 Oct 2017 15:16:45 +0200 > > > From: Roman Yurchak <rth.yurc...@gmail.com > > > <mailto:rth.yurc...@gmail.com>> > > > To: Scikit-learn mailing list <scikit-learn@python.org > > > <mailto:scikit-learn@python.org>> > > > Subject: Re: [scikit-learn] unclear help file for > > > ? ? ? ? sklearn.decomposition.pca > > > Message-ID: <b2abdcfd-4736-929e-6304-b93832932...@gmail.com > > > <mailto:b2abdcfd-4736-929e-6304-b93832932...@gmail.com > >> > > > Content-Type: text/plain; charset=utf-8; format=flowed > > > > > > Ismael, > > > > > > as far as I saw the sklearn.decomposition.PCA doesn't mention > > > scaling at > > > all (except for the whiten parameter which is post-transformation > > > scaling). > > > > > > So since it doesn't mention it, it makes sense that it doesn't > do any > > > scaling of the input. Same as np.linalg.svd. > > > > > > You can verify that PCA and np.linalg.svd yield the same > results, with > > > > > > ``` > > > ?>>> import numpy as np > > > ?>>> from sklearn.decomposition import PCA > > > ?>>> import numpy.linalg > > > ?>>> X = np.random.RandomState(42).rand(10, 4) > > > ?>>> n_components = 2 > > > ?>>> PCA(n_components, > svd_solver='full').fit_transform(X) > > > ``` > > > > > > and > > > > > > ``` > > > ?>>> U, s, V = np.linalg.svd(X - X.mean(axis=0), > full_matrices=False) > > > ?>>> (X - X.mean(axis=0)).dot(V[:n_components].T) > > > ``` > > > > > > -- > > > Roman > > > > > > On 16/10/17 03:42, Ismael Lemhadri wrote: > > > > Dear all, > > > > The help file for the PCA class is unclear about the > preprocessing > > > > performed to the data. > > > > You can check on line 410 here: > > > > > > > > https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410 > > > < > https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410> > ; > > > > > > > < > https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410 > > > < > https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/decomposition/pca.py#L410>> > ; > > > > that the matrix is centered but NOT scaled, before > performing the > > > > singular value decomposition. > > > > However, the help files do not make any mention of it. > > > > This is unclear for someone who, like me, just wanted to > compare > > > that > > > > the PCA and np.linalg.svd give the same results. In academic > > > settings, > > > > students are often asked to compare different methods and to > > > check that > > > > they yield the same results. I expect that many students > have > > > confronted > > > > this problem before... > > > > Best, > > > > Ismael Lemhadri > > > > > > > > > > > > _______________________________________________ > > > > scikit-learn mailing list > > > > scikit-learn@python.org <mailto:scikit-learn@python.org > > > > > > https://mail.python.org/mailman/listinfo/scikit-learn > > > <https://mail.python.org/mailman/listinfo/scikit-learn> > > > > > > > > > > > > > > > > ------------------------------ > > > > > > Message: 3 > > > Date: Mon, 16 Oct 2017 15:27:48 +0200 > > > From: Serafeim Loukas <seral...@gmail.com <mailto: > seral...@gmail.com>> > > > To: scikit-learn@python.org <mailto:scikit-learn@python.org > > > > > Subject: [scikit-learn] Question about LDA's coef_ attribute > > > Message-ID: <58c6d0da-9de5-4ef5-97c1-48159831f...@gmail.com > > > <mailto:58c6d0da-9de5-4ef5-97c1-48159831f...@gmail.com > >> > > > Content-Type: text/plain; charset="us-ascii" > > > > > > Dear Scikit-learn community, > > > > > > Since the documentation of the LDA > > > ( > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html > > > < > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html> > ; > > > < > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html > > > < > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html>> > ;) > > > is not so clear, I would like to ask if the lda.coef_ attribute > > > stores the eigenvectors from the SVD decomposition. > > > > > > Thank you in advance, > > > Serafeim > > > -------------- next part -------------- > > > An HTML attachment was scrubbed... > > > URL: > > > < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/4263df5c/attachment-0001.html > > > < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/4263df5c/attachment-0001.html>> > ; > > > > > > ------------------------------ > > > > > > Message: 4 > > > Date: Mon, 16 Oct 2017 16:57:52 +0200 > > > From: Alexandre Gramfort <alexandre.gramf...@inria.fr > > > <mailto:alexandre.gramf...@inria.fr>> > > > To: Scikit-learn mailing list <scikit-learn@python.org > > > <mailto:scikit-learn@python.org>> > > > Subject: Re: [scikit-learn] Question about LDA's coef_ attribute > > > Message-ID: > > > ? ? ? ? > > > & > lt;cadeotzricoqhuhjmmw2z14cqffeqyndyoxn-ogkavtmq7v0...@mail.gmail.com > > > <mailto: > cadeotzricoqhuhjmmw2z14cqffeqyndyoxn-ogkavtmq7v0...@mail.gmail.com>> > > > Content-Type: text/plain; charset="UTF-8" > > > > > > no it stores the direction of the decision function to match the > > > API of > > > linear models. > > > > > > HTH > > > Alex > > > > > > On Mon, Oct 16, 2017 at 3:27 PM, Serafeim Loukas > > > <seral...@gmail.com <mailto:seral...@gmail.com>> > wrote: > > > > Dear Scikit-learn community, > > > > > > > > Since the documentation of the LDA > > > > > > > ( > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html > > > < > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html> > ;) > > > > is not so clear, I would like to ask if the lda.coef_ > attribute > > > stores the > > > > eigenvectors from the SVD decomposition. > > > > > > > > Thank you in advance, > > > > Serafeim > > > > > > > > _______________________________________________ > > > > scikit-learn mailing list > > > > scikit-learn@python.org <mailto:scikit-learn@python.org > > > > > > https://mail.python.org/mailman/listinfo/scikit-learn > > > <https://mail.python.org/mailman/listinfo/scikit-learn> > > > > > > > > > > > > > ------------------------------ > > > > > > Message: 5 > > > Date: Mon, 16 Oct 2017 17:02:46 +0200 > > > From: Serafeim Loukas <seral...@gmail.com <mailto: > seral...@gmail.com>> > > > To: Scikit-learn mailing list <scikit-learn@python.org > > > <mailto:scikit-learn@python.org>> > > > Subject: Re: [scikit-learn] Question about LDA's coef_ attribute > > > Message-ID: <413210d2-56ae-41a4-873f-d171bb365...@gmail.com > > > <mailto:413210d2-56ae-41a4-873f-d171bb365...@gmail.com > >> > > > Content-Type: text/plain; charset="us-ascii" > > > > > > Dear Alex, > > > > > > Thank you for the prompt response. > > > > > > Are the eigenvectors stored in some variable ? > > > Does the lda.scalings_ attribute contain the eigenvectors ? > > > > > > Best, > > > Serafeim > > > > > > > On 16 Oct 2017, at 16:57, Alexandre Gramfort > > > <alexandre.gramf...@inria.fr <mailto: > alexandre.gramf...@inria.fr>> > > > wrote: > > > > > > > > no it stores the direction of the decision function to > match the > > > API of > > > > linear models. > > > > > > > > HTH > > > > Alex > > > > > > > > On Mon, Oct 16, 2017 at 3:27 PM, Serafeim Loukas > > > <seral...@gmail.com <mailto:seral...@gmail.com>> > wrote: > > > >> Dear Scikit-learn community, > > > >> > > > >> Since the documentation of the LDA > > > >> > > > ( > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html > > > < > http://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html> > ;) > > > >> is not so clear, I would like to ask if the lda.coef_ > attribute > > > stores the > > > >> eigenvectors from the SVD decomposition. > > > >> > > > >> Thank you in advance, > > > >> Serafeim > > > >> > > > >> _______________________________________________ > > > >> scikit-learn mailing list > > > >> scikit-learn@python.org <mailto: > scikit-learn@python.org> > > > >> https://mail.python.org/mailman/listinfo/scikit-learn > > > <https://mail.python.org/mailman/listinfo/scikit-learn> > > > >> > > > > _______________________________________________ > > > > scikit-learn mailing list > > > > scikit-learn@python.org <mailto:scikit-learn@python.org > > > > > > https://mail.python.org/mailman/listinfo/scikit-learn > > > <https://mail.python.org/mailman/listinfo/scikit-learn> > > > > > > -------------- next part -------------- > > > An HTML attachment was scrubbed... > > > URL: > > > < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/505c7da3/attachment.html > > > < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/505c7da3/attachment.html>> > ; > > > > > > ------------------------------ > > > > > > Subject: Digest Footer > > > > > > _______________________________________________ > > > scikit-learn mailing list > > > scikit-learn@python.org <mailto:scikit-learn@python.org> > > > https://mail.python.org/mailman/listinfo/scikit-learn > > > <https://mail.python.org/mailman/listinfo/scikit-learn> > > > > > > > > > ------------------------------ > > > > > > End of scikit-learn Digest, Vol 19, Issue 25 > > > ******************************************** > > > > > > > > > > > > > > > _______________________________________________ > > > scikit-learn mailing list > > > scikit-learn@python.org > > > https://mail.python.org/mailman/listinfo/scikit-learn > > > > -------------- next part -------------- > > An HTML attachment was scrubbed... > > URL: < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/f47e63a9/attachment.html> > ; > > > > ------------------------------ > > > > Subject: Digest Footer > > > > _______________________________________________ > > scikit-learn mailing list > > scikit-learn@python.org > > https://mail.python.org/mailman/listinfo/scikit-learn > > > > > > ------------------------------ > > > > End of scikit-learn Digest, Vol 19, Issue 28 > > ******************************************** > > > > > > > _______________________________________________ > > scikit-learn mailing list > > scikit-learn@python.org > > https://mail.python.org/mailman/listinfo/scikit-learn > > > > > > > -------------- next part -------------- > An HTML attachment was scrubbed... > URL: < > http://mail.python.org/pipermail/scikit-learn/attachments/20171016/620a9401/attachment.html > > > > ------------------------------ > > Subject: Digest Footer > > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn > > > ------------------------------ > > End of scikit-learn Digest, Vol 19, Issue 31 > ******************************************** > -- Sent from a mobile phone and may contain errors
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