CouplingAnalysis.get_nearest_neighbors() is currently only used as a helper method for CouplingAnalysis.mutual_information() and CouplingAnalysis.information_transfer() and tested indirectly through those. After having ported the underlying C method to Cython in #195, it appeared sensible to gain more confidence on its correct functionality by giving it a test of its own.
To create a test fixture and an expected result to compare to, it is essential to understand what the method is actually supposed to do. In trying that, I found that it has redundant loops and variables defined in several places that at least make it hard to read (see my commentshere; the code appears to be adapted from a more generally applicable algorithm, but has lost its wider applicability anyway due to the adaptations).
I mostly grasped its functionality by now, but still don't really understand the special role of the z dimension given to it by the above mentioned methods it's used by. Other than that, here's what so far I found CouplingAnalysis.get_nearest_neighbors() to be currently doing:
given:
$X = (x(t), y(t), z(t))$: an array of 3 timeseries with length $T$
$d_{xyz}$: an array to indicate, where each timeseries is located within the array (depending on each timeseries' dimensions)
$k$: number of nearest neighbors to look for
NOTE: the dimension of $X_i$ is 1 for all use cases within CouplingAnalysis, except for $z(t)$, which will be either left empty in mutual_information(), or can be of dimension > 1 in information_transfer()
For all times $t = 1,...,T$:
find the $k$ times $t' = 1,...,T$ where in all timeseries $X_i(t')$ is closest to $X_i(t)$,
out of all those $k$ times $t'$, find the biggest of these distances within any timeseries as $\epsilon_{max}$
then, for all timeseries $X_i = x,y,z$:
count how many times that timeseries itself is within $\epsilon_{max}$ to $X_i$ (might be more (or also less?) often then $k$-times),
although neighbors $t'$ within $x$ and $y$ are only counted, if $z$ has a neighbor at the same time $t'$
Still not sure if that's what it is supposed to be doing though. Probably the referenced papers Kraskov (2004) and Runge (2012b) should be consulted.
CouplingAnalysis.get_nearest_neighbors()is currently only used as a helper method forCouplingAnalysis.mutual_information()andCouplingAnalysis.information_transfer()and tested indirectly through those. After having ported the underlying C method to Cython in #195, it appeared sensible to gain more confidence on its correct functionality by giving it a test of its own.To create a test fixture and an expected result to compare to, it is essential to understand what the method is actually supposed to do. In trying that, I found that it has redundant loops and variables defined in several places that at least make it hard to read (see my comments here; the code appears to be adapted from a more generally applicable algorithm, but has lost its wider applicability anyway due to the adaptations).
I mostly grasped its functionality by now, but still don't really understand the special role of the
zdimension given to it by the above mentioned methods it's used by. Other than that, here's what so far I foundCouplingAnalysis.get_nearest_neighbors()to be currently doing:Still not sure if that's what it is supposed to be doing though. Probably the referenced papers Kraskov (2004) and Runge (2012b) should be consulted.