R help - Feb 2003 - lda on curves

I'm working on a rather interesting consulting problem with a client. A 
number of physical variables are measured on a number of cricket bowlers 
in the performance of a delivery. An example variable might be a 
directional component of angular momentum for a particular joint 
measured at a large number (101) of equally spaced timepoints.

Each bowler generates a (fairly smooth) curve for each variable 
measured. I decided to represent each curve by a few orthogonal 
polynomial constrasts.

There are 4 groups of bowlers corresponding to various speeds of 
delivery. I want to use canonical variant analysis to find linear 
combinations of my transformed variables discriminating well between the 
groups of bowlers.

I used lda() from the MASS library to do this, but examining the output 
I notice that the higher-order orthogonal polynomials are getting larger 
coefficients than the more important lower-order ones. This is clearly 
because some scaling of the variables is being done by lda(), and 
because the higher-order polynomial vaiable values are smaller, they are 
scaled up.

I would like to turn off this scaling as it is not what is needed in 
this problem and will cause the tail to "wag the dog". There is no 
obvious parameter to do this in

lda(x,   grouping, prior = proportions, tol = 1.0e-4,
                    subset, na.action = na.fail,
                    method, CV = FALSE, nu)

so I thought that I might try a hack. However:

 > lda
function (x, ...)
{
     if (is.null(class(x)))
         class(x) <- data.class(x)
     UseMethod("lda", x, ...)
}

which isn't very helpful.

Any ideas about how to perform an unscaled canonical variates analysis?

Cheers,

Murray
-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    +64 7 849 6486 home    Mobile 021 1395 862

Hi,

I recently work about linear dimension reduction for classification.
There is a research report on
ftp://ftp.stat.math.ethz.ch/Research-Reports/108.html
In this report I discuss nine methods for linear dimension reduction, five
of which are new. Four of the methods do not perform "internal
scaling" which
you want to avoid. Two of these have been published before by other
authors. The coordinates are
Young, Marco and Odell, Journal of Statistical Planning and Inference, 17
(1987), 307-319
and
Hastie and Tibshirani, IEEE Transactions on Pattern Analysis and Machine
Intelligence, 18 (1996), 607-616.
I have R functions for all the methods, but I don't want to make them open
before the corresponding paper is published. If you are interested, please
contact me off list.
There is more literature about "unscaled canonical variates"
especially by
W. Krzanowski, two references are
Krzanowski, Journal of Chemometrics, 9 (1995), 509-520
Kiers and Krzanowski in Gaul, Opitz and Schader (Eds.) Data Analysis,
Springer, Berlin 2000, 207-218.

Best,
Christian

On Mon, 17 Feb 2003, Murray Jorgensen wrote:
> I'm working on a rather interesting consulting problem with a client. A
> number of physical variables are measured on a number of cricket bowlers 
> in the performance of a delivery. An example variable might be a 
> directional component of angular momentum for a particular joint 
> measured at a large number (101) of equally spaced timepoints.
> 
> Each bowler generates a (fairly smooth) curve for each variable 
> measured. I decided to represent each curve by a few orthogonal 
> polynomial constrasts.
> 
> There are 4 groups of bowlers corresponding to various speeds of 
> delivery. I want to use canonical variant analysis to find linear 
> combinations of my transformed variables discriminating well between the 
> groups of bowlers.
> 
> I used lda() from the MASS library to do this, but examining the output 
> I notice that the higher-order orthogonal polynomials are getting larger 
> coefficients than the more important lower-order ones. This is clearly 
> because some scaling of the variables is being done by lda(), and 
> because the higher-order polynomial vaiable values are smaller, they are 
> scaled up.
> 
> I would like to turn off this scaling as it is not what is needed in 
> this problem and will cause the tail to "wag the dog". There is
no
> obvious parameter to do this in
> 
> lda(x,   grouping, prior = proportions, tol = 1.0e-4,
>                     subset, na.action = na.fail,
>                     method, CV = FALSE, nu)
> 
> so I thought that I might try a hack. However:
> 
>  > lda
> function (x, ...)
> {
>      if (is.null(class(x)))
>          class(x) <- data.class(x)
>      UseMethod("lda", x, ...)
> }
> 
> which isn't very helpful.
> 
> Any ideas about how to perform an unscaled canonical variates analysis?
> 
> Cheers,
> 
> Murray
> 
-- 
***********************************************************************
Christian Hennig
Seminar fuer Statistik, ETH-Zentrum (LEO), CH-8092 Zuerich (currently)
and Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at stat.math.ethz.ch, http://stat.ethz.ch/~hennig/
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
#######################################################################
ich empfehle www.boag.de