How about including the scaling that people might want to use in the User Guide examples?
Raphael On 17 October 2017 at 16:40, Andreas Mueller <t3k...@gmail.com> wrote: > In general scikit-learn avoids automatic preprocessing. > That's a convention to give the user more control and decrease surprising > behavior (ostensibly). > So scikit-learn will usually do what the algorithm is supposed to do, and > nothing more. > > I'm not sure what the best way do document this is, as this has come up with > different models. > For example the R wrapper of libsvm does automatic scaling, while we apply > the SVM. > > We could add "this model does not do any automatic preprocessing" to all > docstrings, but that seems > a bit redundant. We could add it to > https://github.com/scikit-learn/scikit-learn/pull/9517, but > that is probably not where you would have looked. > > Other suggestions welcome. > > > On 10/16/2017 03:29 PM, Ismael Lemhadri wrote: > > 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 >> <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: >> >> > ? ? ? ? >> >> > >> <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 > > > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn > > > > _______________________________________________ > scikit-learn mailing list > scikit-learn@python.org > https://mail.python.org/mailman/listinfo/scikit-learn > _______________________________________________ scikit-learn mailing list scikit-learn@python.org https://mail.python.org/mailman/listinfo/scikit-learn
