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re: about MDSM, trend, and tangent
Hi, friends,
I am forwarding a communication with a distinguished professor for
interested reader in this list. It summarized MDSM well.
Thank you. Oppen discussion is welcome.
Jay Bai
MDSM Research
P.O.Box 272628
Fort Collins, CO 80527
USA
===============
Dear Professor,
Thank you for your response and explanation.
MDSM stand for Multi-Dimensional Sphere Model.
It projects the points in multivariable space onto the unit
hypersphere, so that people can keep the information in all the
dimensions. As each individual species may carry a unique
important information about the system/vegetation.
Furthermore, the projection of the unit vector onto the m-dimensions,
i.e., the m-cosine vector, expresses the relative composition of
system/vegetation. Therefore the cluster analysis can be conducted.
Further, furthermore, If there are two sequential points on the
hypersphere, i.e., two sequential m-vector, then the arc/line/trace
/tangent of the centroid m-vector/ will show the move/dynamic of
the system/vegetation.
Therefore, we can use this model to monitor the change of the
vegetation/system, by investigating the unit m-vector rotating in
the m-space. Also, it can be used to project the future states.
By MDSM, the m dimension information was transformed to cosine
m-vector/tangent m-vector. These m-vectors are m*1 matrix, i.e., can
be considered as m values in one dimension. Thus we successfully
project the m-dimension data onto one dimension and still keep
most/all of the information.
If you are interested, I would be happy to mail you my essay.
Thank you for you attention and reply.
Jay Bai
MDSM Research
P.O.Box 272628
Fort Collins, CO 80527
USA
=========================================
Appendix: Tangent and Instantaneous Trend
Tangent = (delta cosine) : -(delta sine), by definition.
Because sine=sqrt(1-cosine^2), and 1 can be considered as the total,
cosine^2 is much less, therefore the tangent may be simplified as:
delta cosine over delta total:
Tangent = (delta cosine) : -(delta total)
On the other hand, MDSM define the instantaneous trend as cosine
ratio over vector length ratio, i.e., total ratio:
t(i,k)=y(i,k)/y(i,k-1) * |y(k-1)|/|y(k)|
= (cosine ratio)
= (component ratio) : (total ratio)^(-1)
So, these two are equivalent (DENG JIA).
Only, the instantaneous trend is more sensitive for the change, the
tangent is more sensitive to the share.
Any comments, especially from the math/statistics/native English
speakers are welcome.