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November 2006

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Subject:
From:
Arnaud Trollé <[log in to unmask]>
Reply To:
Classification, clustering, and phylogeny estimation
Date:
Tue, 28 Nov 2006 10:34:49 +0100
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Thank you very much for your help Doug,

I would just have a few last uncertainties to dispel, concerning the
comparison of 2 MDPREF spaces:

> For MDPREF any nonsingular linear transformation
> is allowed to be applied to one set (say, the
> stimuli),
Does this include rigid translation ?

> If the transformation matrix is orthogonal, the inverse adjoint of the
> matrix is the matrix itself-- so if an orthogonal
> transformation is applied to the stimuli (say)
> the same orthogonal transformation is applied to
> the vectors-- simply rigidly rotating the entire
> configuration without changing relationships
> among the geometric entities involved.
Is the range of orthogonal transformations limited to only the rigid
rotation ?

In case of dilatation (uniform like for INDSCAL ?), does it make sense to
apply the ''inverse adjoint'' to the set of subject vectors associated to
the dilated set of stimuli, thus obtaining some vectors longer/shorter than
the unit length ? i.e. Should the comparison be based on the two sets of
vectors with their respective different lengths or does it make more sense
to leave the subject vectors associated to the dilated set of stimuli
normalized ?


Thanks again in advance,

Best regards,
Arnaud.

----- Original Message -----
From: "J. Douglas Carroll" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, November 27, 2006 11:13 PM
Subject: Re: Procrustes transformations allowed for comparison of 2 INDSCAL
outcomes ? of two MDPREF outcomes ?


For INDSCAL, the only transformations allowed are
permutations, possible reflections of axes, and
uniform dilations (multiplication of all
coordinates by the same positive constant).

For MDPREF any nonsingular linear transformation
is allowed to be applied to one set (say, the
stimuli), while the "inverse adjoint" of that
transformation should be applied to the other set
(in this case, the subject vectors).  The inverse
adjoint is simply the inverse of the transpose of
the matrix involved.

Best,

Doug Carroll

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