Re: how to compute distance metrics with multi dimensional data

From: Lou Pecora (pecora_at_anvil.nrl.navy.mil)
Date: 02/10/05 

Date: Thu, 10 Feb 2005 16:23:09 -0500

In article <1108056923.446663.200310@g14g2000cwa.googlegroups.com>,
 "bluelagoon" <bluelagoontrading@hotmail.com> wrote:

> i don't think it's important whether it's sensor data, needs
> calibration or normalization, where the data comes from, etc...it's
> simply not relevent here at all... except that i have 2-d times series.
>
> ok suppose
> a(n) = amplitude of a cycle n measured in points, d(n) = duration of
> a(n) cycle measured in units, points are not units... and n = 1000 ie i
> have 1000 row samples of a,d data...
> again times series at T is simply a pair(two element vector)
> amplitude(points) and duration(units) a,d a and d are different
> measurement units of the same phenomenon.
>
> i embed the pair dim=4 delay = 1 as, here shown separately as ampl. and
> dur.
> a1,a2,a3,a4 d1,d2,d3,d4
> a2,a3,a4,a5 d2,d3,d4,d5
> a3,a4,a5,a6 d3,d4,d5,d6
>
> or i can write it in pairs as, here shows as a pair ampl. and dur.
> a1,d1 a2,d2, a3,d3 a4,d4 row1 for dim=4 delay = 1
> a2,d2, a3,d3 a4,d4 a5,d5 row2
> a3,d3, a4,d4, a5,d5 a6,d6 row3
> .... for all 1000 rows
>
>
> all i want is to know how to compute distances between the rows or 2d
> embedded data...
>
> please help out if you can...
> thanks.

I'm not sure I get it, but I would go back to what I said before. You
want to demean the each time series and scale it to the standard
deviation. That puts all data on the same footing since units are not
important. Then just use the Euclidean metric.

You didn't say what the distances will be used for or I missed it.

-- Lou Pecora (my views are my own)