[SciPy-User] synchronizing timestamps from different systems; unpaired linear regression
Thu Apr 12 02:00:53 CDT 2012
There have many good suggestions, I will add another. One option would
be to model this via dynamic programming. I think searching for
"sequence alignment" and "time warping" will give you a lot of helpful
The basic idea is that one models sequence-B to be a modification of
sequence-A where "tokens" could have been added, deleted or perturbed
by noise (all modeled as statistically independent of each other) and
that there is a transformation that connects the indices of the two
Computationally this is potentially costlier but you can get to the
global minimum if the time warp wasnt there. It does reasonably well
even if it is.
Regarding previous suggestions:
If you have some periodicity in the signals, then computing
autocorrelation on the two streams will also give you an idea of whats
the slew rate between the clocks and cross-correlation will point
towards an offset once you have accounted for the slew rate. (All this
is assuming there arent too many 'adds' and 'deletes'). The numbers
you will get will not be exact but perhaps a good point to initialize
your algorithm with.
On Tue, Apr 10, 2012 at 11:16 PM, Chris Rodgers <firstname.lastname@example.org> wrote:
> Dear all
> Thanks very much for the suggestions!
> Re a new hardware implementation: I bet this would totally work and
> honestly is probably the fastest way to get it working. I think even a
> rough system clock would do the trick. The downsides are 1) many data
> have already been collected with the old setup; 2) I'm getting
> stubbornly interested in this problem for its own sake since it feel
> so solvable. So perhaps I'll change the hardware for future data and
> keep working on algorithms for the old data. (I'd never heard of
> Lamport timestamps. The wikipedia article is really interesting. If I
> understand it correctly, it would still require a hardware change
> Re Nathaniel's suggestion:
> I think this is pretty similar to the algorithm I'm currently using. Pseudocode:
> current_guess = estimate_from_correlation(x, y)
> for timescale in decreasing_order:
> xm, ym = find_matches(
> x, y, current_guess, within=timescale)
> current_guess = linfit(xm, ym)
> The problem is the local minima caused by mismatch errors. If the
> clockspeed estimate is off, then late events are incorrectly matched
> with a delay of one event. Then the updated guess moves closer to this
> incorrect solution. So by killing off the points that disagree, we
> reinforce the current orthodoxy!
> Actually the truest objective function would be the number of matches
> within some specified error.
> ERR = .1
> def objective(offset, clockspeed):
> # adjust parametrization to suit
> adj_y_times = y_times * clockspeed + offset
> closest_x_times = np.searchsorted(x_midpoints, adj_y_times)
> pred_err = abs(adj_y_times - x_midpoints[closest_x_times])
> closest_good = closest_x_times[pred_err < ERR]
> return len(unique(closest_good))
> That function has some ugly non-smoothness due to the
> len(unique(...)). Would something like optimize.brent work for this or
> am I on the wrong track?
> Thanks again all!
> On Tue, Apr 10, 2012 at 2:22 PM, Nathaniel Smith <email@example.com> wrote:
>> On Tue, Apr 10, 2012 at 10:18 PM, Nathaniel Smith <firstname.lastname@example.org> wrote:
>>> return np.sum((y_times - x_times[closest_x_times]) ** 2)
>> On further thought, squaring is probably exactly the wrong
>> transformation here -- squared error focuses on minimizing the large
>> errors, and in this case we know that the large errors are caused by
>> events that got dropped on the X side, and that these contain no
>> information about the proper (offset, clockspeed).
>> np.sqrt(np.abs(...)) would probably do better, or something similar
>> that flattens out for larger values. Easy to play around with, though.
>> Also on further thought, it might make sense to run that both
>> directions, and match x values against y values too.
>> -- Nathaniel
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