I've been upgrading my SADI code for lifecourse sequence analysis in #Stata (categorical time-series stuff, in effect).
As a side exercise I adapted the TWED distance measure for continuous variables, not just categorical. Time Warp Edit Distance stretches and compresses the time axis to calculate similarity in time-series, allowing recognition of similarity displaced in time (with penalisation).
Here I cluster country-level COVID19 data, specifically per-million daily death rates.
Geography represents many things: clearly networks of travel and transmission, but also cultural and economic similarity. Quality of data may matter too: some of the poorer countries in cluster 1 may simply have not identified C19 deaths as much as richer countries (many of the poorest countries don't report any data).
Some clusters show much more marked temporal similarity (7 & 8 high, 1 pretty low).
An addendum: TWED measures similarity between time-series, allowing a certain amount of "alignment", i.e., recognising similarity that is near in time, but not at the same time (though penalising this displacement). It's good at recognising peaks that happen at about but not exactly the same time.
Running a conventional analysis (just summing the day-by-day difference) on the same data yields poorer results.
More thoughts. TWED compresses/stretches time locally to detect matches displaced a little in time. We can check for the max displacement. This pair (Moldova and Chile) have a max displacement between 75 and 100 days. Clearly it's because of the late spike, due to crude updates to the figures.
In this case TWED is suboptimal: it's putting these 2 closer because of blips. But very few pairs have such a big displacement.
So MD and CL have a displacement of 75-100 days. Two more pairs have one of 30-40.
But only 1104 (of 7381 distinct pairs) have a displacement of 3+ days.
Only 2425 of 7381 pairs have a displacement of 1 day or more. {edit}
That is, in the main TWED does relatively little time-warping, but yet gives a much better result.
If we compare the unrestricted TWED distances with ones with a limit of 9 days' warping, the correlation is 0.999999. Despite the MD/CL example, practically all the important warping is within this small span.
On the other hand, the correlation between TWED and a no-warping comparison (i.e., a simple Euclidean comparison of day by day distances), the correlation is 0.836202: a pretty big difference. If we allow even 1 day of warping, the correlation with pure TWED is 0.999983.
Brendan Halpin