# Re: \$c1 in dudi.acm - what is it?

From: Stéphane Dray (dray@biomserv.univ-lyon1.fr)
Date: Fri Dec 02 2005 - 09:22:14 MET

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c1, in a dudi object is the principal axis.
it is the eigenvector of XtDXQ for a trplet (X,Q,D).

In a geometric point of view, If you project the table on the principal
axis, you obtain the coordinates of row (li) :
>
CS1 CS2 CS3
1 -0.37311477 -0.08991481 0.3374628
2 -0.47534561 0.05563494 0.3273491
3 -0.35874481 -0.24635950 0.1678597
4 -0.41502999 -0.10017110 -0.3041156
5 -0.02083430 -0.90296663 0.2221809
6 -0.38118633 -0.15259585 -0.0482375
NULL
Axis1 Axis2 Axis3
1 -0.37311477 -0.08991481 0.3374628
2 -0.47534561 0.05563494 0.3273491
3 -0.35874481 -0.24635950 0.1678597
4 -0.41502999 -0.10017110 -0.3041156
5 -0.02083430 -0.90296663 0.2221809
6 -0.38118633 -0.15259585 -0.0482375
Symmetrically, you have the principal component (l1). (Duality diagram)
c1 are eigenvector of unit norm, when co contain vectors with lambda
norm (lambda is the associated eigenvalue).
Another point of view is to say that c1 are loadings. c1 is a vector of
coefficient of unit norm to obtain linear combination of variables that
maximise the variance of the observation (li).

Kent wrote:

> My question is about dudi.acm and \$c1.
>
> Output from a dudi.acm:
>
> [quote]
>
> Duality diagramm
>
> class: acm dudi
>
> \$call: dudi.acm(banque)
>
> vector length mode content
>
> 1 \$cw 73 numeric column weights
>
> 2 \$lw 810 numeric row weights
>
> 3 \$eig 52 numeric eigen values
>
> data.frame nrow ncol content
>
> 1 \$tab 810 73 modified array
>
> 2 \$li 810 3 row coordinates
>
> 3 \$l1 810 3 row normed scores
>
> 4 \$co 73 3 column coordinates
>
> 5 \$c1 73 3 column normed scores
>
> other elements: cr
>
> [/quote]
>
> What is c1? It says 'column normed scores' but I think it is coordinates.
>
> I can plot c1, for example like this: 's.arrow(banque.acm\$c1)'. So, \$c1
>
> must be coordinates?
>
> I guess, what I want is just the coordinates (to plot a nice figure
>
> with column dots).
>
> And perhaps all I need is \$co. But I am curious... what is \$c1?
>
> I have tried to read helpfiles in R and documentation on the net, for
>
> Sincerely
>
> //Kent Lofgren
>
> Dept. of Educational Measurement, Umea University
>
> Address: Umea Univ., BVM, SE-90187 Umea
>
> SWEDEN
>
> Telephone: +46 (0)90-786 95 26
>
> Mobile: +46 (0)70-333 80 46
>
> E-mail: kent.lofgren@edmeas.umu.se
>
> URL: www.umu.se/edmeas/bologna/index_eng.html
>

```--
Stéphane DRAY (dray@biomserv.univ-lyon1.fr )
Laboratoire BBE-CNRS-UMR-5558, Univ. C. Bernard - Lyon I
43, Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
Tel: 33 4 72 43 27 57       Fax: 33 4 72 43 13 88
http://www.steph280.freesurf.fr/
```

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