Re: how to compute distance metrics with multi dimensional data

From: bluelagoon (bluelagoontrading_at_hotmail.com)
Date: 02/10/05

  • Next message: Lou Pecora: "Re: how to compute distance metrics with multi dimensional data" 
    Date: 10 Feb 2005 09:35:23 -0800

    Lou Pecora wrote:
    > In article <1108038987.525148.3280@l41g2000cwc.googlegroups.com>,
    > "bluelagoon" <bluelagoontrading@hotmail.com> wrote:
    >
    > > i got a set of time series data that is 1000 rows by 2 columns.
    > > column 1 contains amplutude data that corresponds! to column 2
    duration
    > > data. ie
    > > a1,d1
    > > a2,d2
    > > ...
    > > a1000, d1000
    > >
    > > now, i embed both columns with dim=4 and delay=1, so i get
    > > a1,a2,a3,a4 d1,d2,d3,d4
    > > a2,a3,a4,a5 d2,d3,d4,d5
    > > a3,a4,a5,a6 d3,d4,d5,d6
    > > ...
    > > so in each row i have two sets if vectors A and D, each j element
    of A
    > > vector corresponds to j element of D vector!, i is the row, j is
    the
    > > column.
    > > A1 = (a1,a2,a3,a4) and D1 = (d1,d2,d3,d4)
    > >
    > > so we get
    > > A1,D1
    > > A2,D2
    > > ...
    > > A1000, D1000
    > >
    > > the question is:
    > > i need to compute the distance across the column, ie between A1,D1
    and
    > > A2,D2 or A1,D1 and A3,D3 ( don't forget that each element of a1
    > > corresponds to d1 etc...) ?
    > > Euclidean, max norm and manhattan?
    > >
    > > basically it's embedded 2-d data.
    > >
    > > also how to generalized this 3-d and N-dim data.
    > >
    > > i would appreciate any help.
    > > thanks.
    >
    > If your data is from sensors or other physical devices then it is not

    > clear that the amplitudes are meaningful unless you have carefully
    > calibrated each measurement. But you have to ask whether having the
    > time series in the units of measurement is important. Since you are
    > trying to get the distances you might have something in mind where
    you
    > can scale one time series to get it on a meaningful scale to compare
    to
    > the other time series. This requires knowledge of the system and
    > depends on what you are trying to compute. So, we need to know more
    > about what it is you are doing.
    >
    > However, if you are trying to reconstruct an attractor from the time
    > series, then you probably want to "normalize" the time series by
    > demeaning each one rescaling each time series to its standard
    deviation.
    > Otherwise you end up comparing meters to joules or whatever in your
    > distances. The rescaling is really just like picking different units
    of
    > the same measurment type (e.g using feet rather than meters). It
    also
    > makes comparisons of distances to attractor size easier to think
    about.
    >
    > -- Lou Pecora (my views are my own)

    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.

  • Next message: Lou Pecora: "Re: how to compute distance metrics with multi dimensional data"

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