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Reverse-engineer fractal resampling process

by deadrabbit
Tags: fractal, process, resampling, reverseengineer
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deadrabbit
#1
Jun30-14, 11:24 PM
P: 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/...resampling.pdf
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berkeman
#2
Jul1-14, 11:35 AM
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P: 40,707
Quote Quote by deadrabbit View Post
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/...resampling.pdf
Why don't you just contact the authors of the work to ask for their help?
AlephZero
#3
Jul1-14, 04:14 PM
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Thanks
P: 6,953
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/stati...pdf/A20n39.pdf

For the "inspiration" on page 7, google fractal (or fractional) brownian terrain generation.


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