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.
Best,
Sebastian
> On Oct 16, 2017, at 3:25 PM, Sebastian Raschka <se.rasc...@gmail.com> wrote:
>
> Hi,
>
> 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
>
> CovMat = \fact{1}{n} \sum_{i=1}^{n} (x_n - \bar{x}) (x_n - \bar{x})^T
>
> where \bar{x} = vector of feature means
>
> So, if you center the data prior to computing the covariance matrix, \bar{x}
> is simply 0.
>
> Best,
> Sebastian
>
>> On Oct 16, 2017, at 2:27 PM, Ismael Lemhadri <lemha...@stanford.edu
>> <mailto:lemha...@stanford.edu>> wrote:
>>
>> @Andreas Muller:
>> My references do not assume centering, e.g.
>> http://ufldl.stanford.edu/wiki/index.php/PCA
>> <http://ufldl.stanford.edu/wiki/index.php/PCA>
>> any reference?
>>
>>
>>
>> On Mon, Oct 16, 2017 at 10:20 AM, <scikit-learn-requ...@python.org
>> <mailto:scikit-learn-requ...@python.org>> wrote:
>> Send scikit-learn mailing list submissions to
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>>
>> 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 <mailto:t3k...@gmail.com>>
>> To: scikit-learn@python.org <mailto:scikit-learn@python.org>
>> Subject: Re: [scikit-learn] unclear help file for
>> sklearn.decomposition.pca
>> Message-ID: <04fc445c-d8f3-a3a9-4ab2-0535826a2...@gmail.com
>> <mailto: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>
>> > <mailto: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>
>> > <mailto: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>
>> > <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>
>> > <mailto: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>
>> > <mailto: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>
>> > <mailto:lemha...@stanford.edu <mailto:lemha...@stanford.edu>>>
>> > To: scikit-learn@python.org <mailto:scikit-learn@python.org>
>> > <mailto: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>
>> > <mailto:18okhcfn0u5dnzj%...@mail.gmail.com
>> > <mailto:18okhcfn0u5dnzj%25...@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/
>> > <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
>> >
>> > <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>
>> >
>> > <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>
>> > <mailto:rth.yurc...@gmail.com <mailto:rth.yurc...@gmail.com>>>
>> > To: Scikit-learn mailing list <scikit-learn@python.org
>> > <mailto:scikit-learn@python.org>
>> > <mailto: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>
>> > <mailto: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>>
>> > >
>> >
>> > <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>
>> > <mailto: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>
>> > <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>
>> > <mailto:seral...@gmail.com <mailto:seral...@gmail.com>>>
>> > To: scikit-learn@python.org <mailto:scikit-learn@python.org>
>> > <mailto: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>
>> > <mailto: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>>
>> >
>> > <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>
>> >
>> > <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>
>> > <mailto:alexandre.gramf...@inria.fr
>> > <mailto:alexandre.gramf...@inria.fr>>>
>> > To: Scikit-learn mailing list <scikit-learn@python.org
>> > <mailto:scikit-learn@python.org>
>> > <mailto: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>
>> >
>> > <mailto: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>
>> > <mailto: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>
>> >
>> > <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>
>> > <mailto: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>
>> > <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>
>> > <mailto:seral...@gmail.com <mailto:seral...@gmail.com>>>
>> > To: Scikit-learn mailing list <scikit-learn@python.org
>> > <mailto:scikit-learn@python.org>
>> > <mailto: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>
>> > <mailto: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>
>> > <mailto: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>
>> > <mailto: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>
>> >
>> > <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>
>> > <mailto: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>
>> > <https://mail.python.org/mailman/listinfo/scikit-learn
>> > <https://mail.python.org/mailman/listinfo/scikit-learn>>
>> > >>
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>> > > scikit-learn mailing list
>> > > scikit-learn@python.org <mailto:scikit-learn@python.org>
>> > <mailto:scikit-learn@python.org <mailto:scikit-learn@python.org>>
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>> > <https://mail.python.org/mailman/listinfo/scikit-learn>
>> > <https://mail.python.org/mailman/listinfo/scikit-learn
>> > <https://mail.python.org/mailman/listinfo/scikit-learn>>
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