Reverse-engineer fractal resampling process

  1. Hey,

    I am working on a project where I need to take several time series of various lengths and identify common features. So, for example, a period of 100 days may exhibit the same features as a period of 10 days -- the system is self-similar in this way.

    In order to compare these series of different lengths I need to strip out noise that is not important for feature identification in order to bring them to the same scale.

    I have come across this document that shows a rather efficient method of doing this and would like to reverse engineer it... any help greatly appreciated.

    http://www.congrexprojects.com/docs...4_12-40_donati-martinez_fractalresampling.pdf
     
  2. jcsd
  3. berkeman

    Staff: Mentor

    Why don't you just contact the authors of the work to ask for their help?
     
  4. AlephZero

    AlephZero 7,298
    Science Advisor
    Homework Helper

    Doesn't page 8 already explain it?

    If the original data set is ##x_0, x_1, \dots##, start by keeping the points ##x_0, x_{2^k}, 2x_{2^k}, \dots## for a "large" value of ##k##.

    If linear interpolation between those points is not good enough in an interval, add the mid-point of that interval to the list of points.

    Rinse and repeat till the result is accurate enough.

    In the example they start from ##x_0## and ##x_8##, then add the mid point ##x_4##, etc.

    You might want to compare this will something like spline fitting adaptive knot placement, e.g. http://www3.stat.sinica.edu.tw/statistica/oldpdf/A20n39.pdf

    For the "inspiration" on page 7, google fractal (or fractional) brownian terrain generation.
     
    Last edited: Jul 1, 2014
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