Reverse-engineer fractal resampling process

[deadrabbit]

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

 

[berkeman]

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

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

 

[AlephZero]

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.