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From: John on 3 Dec 2005 16:54
Hi

I have a 10-dimensional vector v(t)=(C1(t),C2(t),......,C10(t)) where Cj(t)
is between 0 and pi for any t.

I let t run from t=0 to t=T and get a set S of vectors
S={v(0),v(1),.....,v(T)}

How do I map this set S into a discrete set D ?

And how do I calculate the probability of any discrete vector in D?

Thanks...



From: NS on 4 Dec 2005 02:39
You first need to define some distortion measure or performance measure
for the mapping. Then, given the distortion measure one may design an
optimal mapping.

John wrote:
> Hi
>
> I have a 10-dimensional vector v(t)=(C1(t),C2(t),......,C10(t)) where Cj(t)
> is between 0 and pi for any t.

OK, this is a curve in a 10 dimensional space.

> I let t run from t=0 to t=T and get a set S of vectors
> S={v(0),v(1),.....,v(T)}

What's that a set of T+1 (quantized?) vectors (centroids?) along the
above curve?

> How do I map this set S into a discrete set D ?

What is the definition of the discrete set D?

> And how do I calculate the probability of any discrete vector in D?

Exactly the same way you calculate the that probability someone would
understand what you were asking...

> Thanks...
for what?
From: John on 4 Dec 2005 06:26

>
>
> What's that a set of T+1 (quantized?) vectors (centroids?) along the above
> curve?

No, it's a set of observations.

>
> What is the definition of the discrete set D?
>

Well. lets just say that the range 0 to pi is mapped into the discrete range
0,0.1,0.2,........3.2




From: Fred Marshall on 4 Dec 2005 14:22

"John" <joehatesspam(a)nospam.spamshit> wrote in message
news:43921415$0$67256$157c6196(a)dreader2.cybercity.dk...
> Hi
>
> I have a 10-dimensional vector v(t)=(C1(t),C2(t),......,C10(t)) where
> Cj(t) is between 0 and pi for any t.

***So v() and Cj() are continuous in time.

>
> I let t run from t=0 to t=T and get a set S of vectors
> S={v(0),v(1),.....,v(T)}

***So now you have sampled v(), eh? It's on a discrete set of time indices.
Or are you suggesting (not so clearly) that S is an infinite set of vectors
v?

>
> How do I map this set S into a discrete set D ?

***Why is S not a discrete set? Actually it would help to define a couple
of things:

T is a positive integer.
N=T ... which may seem trivial but helps the notation be more typical where
there are N+1 elements in S:

S={v(0),v(T/N),.....v(T-T/N),v(T)}

The v(j) terms are all on discrete times and, thus are vectors:

v(j) = (C1(j),C2(j),......,C10(j)).

So the v() here are vectors of length 10 and S is a matrix that is 10 X
(N+1)T no???

Fred


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