Fix conversion of time-series into sequence for lempel_ziv_complexity

[kempa-liehr]

This pull fixes the bin boundaries such that the very first bin contains a reasonable number of time-series value.
While this fix has a nearly neglectable impact on the test cases, it significantly changes the feature value for real-world applications and improves the feature's interpretability.

[nils-braun]

Thanks @kempa-liehr. I think the failing tests are unrelated (but something we should have a look into nevertheless).

[MaxBenChrist]

can we merge this?

[MaxBenChrist]

I have the feeling that this is not an efficient implementation.

If we want to count the occurrence of substrings, we can use a counter for collections (collections.Counter). If we want to count the amount of different substrings, we can just call set on the list of substrings, without the loop

[nils-braun]

But lemel_ziv isn't neither the amount of fixed-length substrings nor the counter of fixed length substrings. The idea behind it is that the length of the substrings is chosen in a way to never have any substring occuring doubled.

Example: 100111
First substring: just 1
Second: just 0
Third: would be 0 again, but we have 0 already so we need to choose 01
Forth: would be 1, but we have 1 already so we need to choose 11
End of the word -> 4 substrings / length 6 = 0.66.

The code is O(n) (the while loop needs approx n steps in in each we have a set check, which is O(1) and some other operations like addition, which are also O(1)), and I do not think we can be asymptotically better than this. There exist cython implementations of that - but as long as those are not accessible easily via conda and pip, I do not see any nice way for us.

Having some compiled (cython/numba) feature calculators would be really nice, but so far no one had time to have a look into this

[MaxBenChrist]

thanks for the explanation nils!

[nils-braun]

I have just merged in the newest changes from main. Let's see if that fixed the failing tests

[codecov-io]

Codecov Report

Merging #806 (98bcd43) into main (26af836) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main     #806   +/-   ##
=======================================
  Coverage   95.92%   95.92%           
=======================================
  Files          18       18           
  Lines        1841     1841           
  Branches      362      362           
=======================================
  Hits         1766     1766           
  Misses         37       37           
  Partials       38       38           

Impacted Files	Coverage Δ
tsfresh/feature_extraction/feature_calculators.py	97.29% <100.00%> (ø)

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 26af836...98bcd43. Read the comment docs.