Re: [scikit-learn] 1. Re: unclear help file for sklearn.decomposition.pca

Mon, 16 Oct 2017 12:40:27 -0700 

It might be useful to have some of these comments in the docs.
Currently the PCA docsting only states that PCA is computed with SVD and then goes on discussing randomized SVD solvers. The user guide is not more helpful on this subject either,
Ismael opened a documentation PR on it in https://github.com/scikit-learn/scikit-learn/pull/9934 

--
Roman

On 16/10/17 21:29, Sebastian Raschka wrote:

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
<mailto: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
any reference?



On Mon, Oct 16, 2017 at 10:20 AM, <scikit-learn-requ...@python.org
<mailto:scikit-learn-requ...@python.org>> wrote:

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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:
    >
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    >     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 --------------
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    >
    >     ------------------------------
    >
    >     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
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    >
    >     ------------------------------
    >
    >     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>>
    >     >>
    >     > _______________________________________________
    >     > scikit-learn mailing list
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    <mailto:scikit-learn@python.org <mailto:scikit-learn@python.org>>
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