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I wanted to use it like the fisher transform but from what I
understand it is better used for smaller sample sets. Maybe using
multiple diminsions or matices it can simulate genetic algorism.
Like parenting. To difference parents combine to generate multiple
outcomes, but only one fits the data the best or maybe forecast
method. Maybe you can't even use the Hotelling Transform for trading
but it is a transform and theoretically it seems possible.
Below is what I read about the Hotelling Transform so I was thinking
that the basis vectors for such a transformation are different for
each image-unlike the Fourier Transform or the DCT which use the
same basis vectors. In this way, the Hotelling Tranformation does
a "best fit" to the image by choosing a basis set that gives optimal
compaction of the information. Could the image some how be the
market data in similar studies of ehlers or even your non-spectral
analysis. Econometric analysis might not be possible, but I hope you
or someone else give it a shot.
Thank you.
=======================
Hotelling Transform
The Fourier Transform and the DCT all use a fixed set of basis
functions for the transformation. What if we chose a set of basis
functions based on the input image itself?
These different transforms all compact the information in the signal
in one form or another, but the optimal compaction of information
comes when we let the image itself tell us which basis functions
give the best compaction.
Suppose that we have a multispectral. Each band of the spectrum has
its own information, but it may be that the most information isn't
found in one image band or another, but in a linear combination of
information from the collective bands. How do we determine this?
One way is to find the covariance matrix C of the pixels. Since C
is real and symmetric, it always has eigenvectors. If we sort the
eigenvalues, we can rank the corresponding eigenvectors. These
eigenvectors indicate the spread of the information content in the
pixels-the eigenvector with the largest variance contains the most
information, the one with the next largest variance contains the
most information if all components of the first one are removed, and
so on until one is left with the eigenvector with the smallest
eigenvalue, which corresponds to the dimension of least information.
Each eigenvector is a linear combination of the original basis
vectors, so the components of each eigenvector indicate how much of
each original image band goes in the optimal mix.
Transforming the image into the coordinate space whose basis vectors
are the eigenvectors of the covariance matrix is called the
Hotelling Transform, sometimes known as the Karhunen-Loeve Transform
or principal-component analysis.
Notice that the basis vectors for such a transformation are
different for each image-unlike the Fourier Transform or the DCT
which use the same basis vectors. In this way, the Hotelling
Tranformation does a "best fit" to the image by choosing a basis set
that gives optimal compaction of the information
=================
--- In equismetastock@xxxxxxxxxxxxxxx, mgf_za_1999 <no_reply@xxxx>
wrote:
> Sorry, I am mixing up two things here, the Hotelling transform and
the
> Hotelling T2 statistic. Both are inherently multidimensional,
which
> is why I am asking the context. I think the Hotelling transform
> entails calculating the eigenvalues - there is this neat way of
doing
> that. You just keep on raising whatever matrix you are working
with
> to higher powers and the eigenvalues sort of fall out. It is
called
> the power technique if I remember correctly. I don't think it is
> doable in MS, since, being multidimensional, you need to work with
> matrices and so on. But again, give the context and maybe I can
help
> a bit.
>
> Regards
> MG Ferreira
> TsaTsa EOD Programmer and trading model builder
> http://www.ferra4models.com
> http://fun.ferra4models.com
>
> --- In equismetastock@xxxxxxxxxxxxxxx, mgf_za_1999 <no_reply@xxxx>
wrote:
> > Could you give the context of the Hotelling transform? I've
never
> > seen the Hotelling T2 statistic used in technical analysis. I
could
> > assist maybe, if I understand how it is used. The Hotelling T2
stat,
> > if this is what you refer to, is usually used in multivariate
analysis
> > but there is a much simpler formula that works in one dimension.
> >
> > Regards
> > MG Ferreira
> > TsaTsa EOD Programmer and trading model builder
> > http://www.ferra4models.com
> > http://fun.ferra4models.com
> >
> >
> > --- In equismetastock@xxxxxxxxxxxxxxx, "formulaprimer"
> > <formulaprimer@xxxx> wrote:
> > > Does anyone have a code for Hotelling Transformfor small
sample sizes
> > > (e.g,: short period lengths say n<25)
> > >
> > > Please do not refer to a pay site for indicators. I am in a
forum
> like
> > > this to get free source codes.
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