[GRASS-dev] Reg i.pca output

[Markus Metz]

On Tue, Mar 26, 2013 at 12:10 PM, Rashad M <mohammedrashadkm at gmail.com> wrote:
>
>
>
> On Tue, Mar 26, 2013 at 3:58 PM, Markus Metz <markus.metz.giswork at gmail.com>
> wrote:
>>
>> On Tue, Mar 26, 2013 at 10:25 AM, Rashad M <mohammedrashadkm at gmail.com>
>> wrote:
>> >
>> >
>> >
>> > On Tue, Mar 26, 2013 at 2:44 PM, Markus Metz
>> > <markus.metz.giswork at gmail.com>
>> > wrote:
>> >>
>> >> On Tue, Mar 26, 2013 at 8:39 AM, Rashad M <mohammedrashadkm at gmail.com>
>> >> wrote:
>> >> > Hi,
>> >> >
>> >> > i.pca creates 6 raster maps for 6 input raster
>> >> >
>> >> > eg:
>> >> >
>> >> > i.pca
>> >> >
>> >> >
>> >> > in=lsat7_2002_10,lsat7_2002_20,lsat7_2002_30,lsat7_2002_40,lsat7_2002_50,lsat7_2002_70
>> >> > \
>> >> >     out=lsat7_2002_pca
>> >> >
>> >> >
>> >> > I have a doubt here
>> >> >
>> >> > Does the output lsat7_2002_pca.1 is the corresponding map for
>> >> > lsat7_2002_10?
>> >>
>> >> No. lsat7_2002_pca.1 contains the principal component with the highest
>> >> eigenvalue and is calculated using all input bands. More generally,
>> >> each lsat7_2002_pca.* map is calculated using all input bands. Look at
>> >> the eigenvectors to find out the weights with which each input map
>> >> contributes to a specific PCA.
>> >>
>> >
>> > So by knowing a pixel value of lsat7_2002_pca.1 can I get the value
>> > before
>> > transformation in PCA.
>> > consider this:
>> > I have two bands B1,B2 and after i.pca I get PC1,PC2. Then is there a
>> > way to
>> > derive value of X,Y where X belongs to B1 and Y belongs to B2 by only
>> > knowing P,Q
>> > where P belongs to PC1 and Q belongs to PC2
>> >
>> > and also X,Y and P,Q are of same index (row,col)
>>
>> X = P * eigenvector(P, X) + P * eigenvector(Q, X) + mean(B1)
>>
>> Using the example from the manual:
>>
>> X = 0.2824 * PC1 + 0.2541 * PC2 + 0.3801 * PC3 +  0.1752 * PC4 -
>> 0.6170 * PC5 - 0.5475 * PC6 + mean(band 1)
>
>
> Thanks.
>
> just a small clarification:
> PC1 is the pixel value at (i,j) of output band  pca.1 and X is the pixel
> value at (i,j) of input band b1
>
> This is correct?

yes

>
>>
>> Markus M
>>
>> >
>> > I hope this is clear
>> >
>> >>
>> >> Markus M
>> >>
>> >> >
>> >> > If so the lsat7_2002_10_pca.1 contains PCA transformed pixel for
>> >> > lsat7_2002_10
>> >> >
>> >> > Is this correct?
>> >> >
>> >> > --
>> >> > Regards,
>> >> >    Rashad
>> >> >
>> >> > _______________________________________________
>> >> > grass-dev mailing list
>> >> > grass-dev at lists.osgeo.org
>> >> > http://lists.osgeo.org/mailman/listinfo/grass-dev
>> >
>> >
>> >
>> >
>> > --
>> > Regards,
>> >    Rashad
>
>
>
>
> --
> Regards,
>    Rashad