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Souradeep Chattapadhyay

2017-Aug-23 21:44 UTC

[R] Scaling Matrix in qda() function in MASS package

Hello,
           I am Souradeep Chattopadhyay and I am a graduate student at Iowa
State University Department of Statistics.

Can anyone please explain the mathematical formulation behind the scaling
matrix returned by the qda function in MASS package. I want to understand
how this scaling matrix is derived from the inputs given to the qda
function.

Example Code

The following example is using the banknote data in the MCLUST package.

*Code*

require(MASS)
require(mclust)
data(banknote)
quad<-qda(banknote[,-1], grouping=banknote$Status, method="mle")
quad$scaling


Scaling matrix returned by qda for this data is

, , counterfeit

                1                    2              3
 4                     5          6
Length   2.853988  1.069414 -0.05279774  0.750531723 -0.2053821  0.6986088
Left        0.000000 -4.208108 -3.04707132 -0.026804815 -0.8644062
-1.1088947
Right      0.000000  0.000000  4.27383763  0.003205759  0.3313675  1.3865888
Bottom   0.000000  0.000000  0.00000000  0.917596063 -0.8707772  0.7274894
Top         0.000000  0.000000  0.00000000  0.000000000 -2.2041415
 0.6956074
Diagonal 0.000000  0.000000  0.00000000  0.000000000  0.0000000-2.1879157

, , genuine

                1                     2               3                4
              5               6
Length  2.592911 -1.169164  0.6105339 -0.3614352 -0.2520496 -0.5281743
Left       0.000000  3.027882  2.2392994 -0.2842368 -1.2092325  0.6927868
Right    0.000000  0.000000 -3.8684746 -0.3972362 -0.4177546 -0.1062555
Bottom 0.000000  0.000000  0.0000000  1.6376150  1.7274240  0.3969998
Top       0.000000  0.000000  0.0000000  0.0000000  2.3022115  0.6318543
Diagonal 0.000000  0.000000  0.0000000  0.0000000  0.0000000  2.4516680



Thanks and Regards

Souradeep

	[[alternative HTML version deleted]]

Bert Gunter

2017-Aug-23 22:58 UTC

head link

[R] Scaling Matrix in qda() function in MASS package

You need to learn how to access code for nonexported methods.  See ?
"::"
> methods(qda)[1] qda.data.frame* qda.default*    qda.formula*    qda.matrix*
see '?methods' for accessing help and source code

Shows you that the methods are not exported from the namespace. Hence
you need to use the triple colon operator to see their code:
> MASS:::qda
Once you have the code, I presume this will answer your question.

Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Wed, Aug 23, 2017 at 2:44 PM, Souradeep Chattapadhyay
<soura at iastate.edu> wrote:> Hello,
>            I am Souradeep Chattopadhyay and I am a graduate student at Iowa
> State University Department of Statistics.
>
> Can anyone please explain the mathematical formulation behind the scaling
> matrix returned by the qda function in MASS package. I want to understand
> how this scaling matrix is derived from the inputs given to the qda
> function.
>
> Example Code
>
> The following example is using the banknote data in the MCLUST package.
>
> *Code*
>
> require(MASS)
> require(mclust)
> data(banknote)
> quad<-qda(banknote[,-1], grouping=banknote$Status,
method="mle")
> quad$scaling
>
>
> Scaling matrix returned by qda for this data is
>
> , , counterfeit
>
>                 1                    2              3
>  4                     5          6
> Length   2.853988  1.069414 -0.05279774  0.750531723 -0.2053821  0.6986088
> Left        0.000000 -4.208108 -3.04707132 -0.026804815 -0.8644062
> -1.1088947
> Right      0.000000  0.000000  4.27383763  0.003205759  0.3313675 
1.3865888
> Bottom   0.000000  0.000000  0.00000000  0.917596063 -0.8707772  0.7274894
> Top         0.000000  0.000000  0.00000000  0.000000000 -2.2041415
>  0.6956074
> Diagonal 0.000000  0.000000  0.00000000  0.000000000  0.0000000-2.1879157
>
> , , genuine
>
>                 1                     2               3                4
>               5               6
> Length  2.592911 -1.169164  0.6105339 -0.3614352 -0.2520496 -0.5281743
> Left       0.000000  3.027882  2.2392994 -0.2842368 -1.2092325  0.6927868
> Right    0.000000  0.000000 -3.8684746 -0.3972362 -0.4177546 -0.1062555
> Bottom 0.000000  0.000000  0.0000000  1.6376150  1.7274240  0.3969998
> Top       0.000000  0.000000  0.0000000  0.0000000  2.3022115  0.6318543
> Diagonal 0.000000  0.000000  0.0000000  0.0000000  0.0000000  2.4516680
>
>
>
> Thanks and Regards
>
> Souradeep
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Ranjan Maitra

2017-Aug-24 19:54 UTC

head link

[R] Scaling Matrix in qda() function in MASS package

I guess the question that is being asked here is what is the scaling matrix that
is being returned in the qda object. The help file on qda() says:
...
scaling: for each group ?i?, ?scaling[,,i]? is an array which transforms
observations so that within-groups covariance matrix is spherical.
...

This is a bit ambiguous. I tried a few cases (spectral, QR decomposition,
especially given that it is an upper triangular matrix) but was unable to match
the result.

Unless someone knows, there is no recourse but to muck through source code.

Btw, I think the following will give the necessary source code:

MASS:::qda.default


Hope this helps!

Best wishes,
Ranjan


On Wed, 23 Aug 2017 15:58:30 -0700 Bert Gunter <bgunter.4567 at gmail.com>
wrote:
> You need to learn how to access code for nonexported methods.  See ?
"::"
> 
> > methods(qda)
> [1] qda.data.frame* qda.default*    qda.formula*    qda.matrix*
> see '?methods' for accessing help and source code
> 
> Shows you that the methods are not exported from the namespace. Hence
> you need to use the triple colon operator to see their code:
> 
> > MASS:::qda
> 
> Once you have the code, I presume this will answer your question.
> 
> Cheers,
> Bert
> 
> 
> Bert Gunter
> 
> "The trouble with having an open mind is that people keep coming along
> and sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip
)
> 
> 
> On Wed, Aug 23, 2017 at 2:44 PM, Souradeep Chattapadhyay
> <soura at iastate.edu> wrote:
> > Hello,
> >            I am Souradeep Chattopadhyay and I am a graduate student at
Iowa
> > State University Department of Statistics.
> >
> > Can anyone please explain the mathematical formulation behind the
scaling
> > matrix returned by the qda function in MASS package. I want to
understand
> > how this scaling matrix is derived from the inputs given to the qda
> > function.
> >
> > Example Code
> >
> > The following example is using the banknote data in the MCLUST
package.
> >
> > *Code*
> >
> > require(MASS)
> > require(mclust)
> > data(banknote)
> > quad<-qda(banknote[,-1], grouping=banknote$Status,
method="mle")
> > quad$scaling
> >
> >
> > Scaling matrix returned by qda for this data is
> >
> > , , counterfeit
> >
> >                 1                    2              3
> >  4                     5          6
> > Length   2.853988  1.069414 -0.05279774  0.750531723 -0.2053821 
0.6986088
> > Left        0.000000 -4.208108 -3.04707132 -0.026804815 -0.8644062
> > -1.1088947
> > Right      0.000000  0.000000  4.27383763  0.003205759  0.3313675 
1.3865888
> > Bottom   0.000000  0.000000  0.00000000  0.917596063 -0.8707772 
0.7274894
> > Top         0.000000  0.000000  0.00000000  0.000000000 -2.2041415
> >  0.6956074
> > Diagonal 0.000000  0.000000  0.00000000  0.000000000 
0.0000000-2.1879157
> >
> > , , genuine
> >
> >                 1                     2               3               
4
> >               5               6
> > Length  2.592911 -1.169164  0.6105339 -0.3614352 -0.2520496 -0.5281743
> > Left       0.000000  3.027882  2.2392994 -0.2842368 -1.2092325 
0.6927868
> > Right    0.000000  0.000000 -3.8684746 -0.3972362 -0.4177546
-0.1062555
> > Bottom 0.000000  0.000000  0.0000000  1.6376150  1.7274240  0.3969998
> > Top       0.000000  0.000000  0.0000000  0.0000000  2.3022115 
0.6318543
> > Diagonal 0.000000  0.000000  0.0000000  0.0000000  0.0000000 
2.4516680
> >
> >
> >
> > Thanks and Regards
> >
> > Souradeep
> >
> >         [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

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