[BUG] Wrong initialisation of TWE distance in _twe_numba.py about sktime HOT 4 OPEN

Yes, exactly outside the permitted band, we should fill the bounding matrix with +inf.

1. I think that this bug could lead to incorrect distance measures, in any case, it can result in spurious analyses.
2. Following the rules to compute the costs, if you have to compute the values in the diagonal cells, you should sum the Euclidean distances both for i,j and i-1, j-1.

    x1 = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0])

    x2 = np.array([10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0])
    
    x1_p = np.insert(x1, 0, 0)
    
    x2_p = np.insert(x2, 0, 0)
    
    dist = 0
    
    for i in range(1, len(x1_p)):
    
        dist += abs(x1_p[i] - x2_p[i]) + abs(x1_p[i-1] - x2_p[i-1])
        
    print(dist)

dist = 86.0

3. I don't think z-scoring the time series in input is mandatory.

from sktime.

I see - I think you are right. Just to clarify, you think it should be filled with +inf outside the permitted band, right?

When we fix this, we should:

• also update the docstrings to be very specific about the output matrix
• ensure to add a test that checks actual against expected for window < 1.0

Further questions:

• TWE distance is a "standard" distance afaik, right? does this mean, it would lead to spurious/incorrect low performance of baselines in predicive performance benchmarking studies?
• can you explain how you obtain 86? I get 44, summing up the Euclidean distances.
• is there perhaps an issue regarding normalization, e.g., by length of series yes/no in th computation? Docstring is not too clear which version of the distance this is, normalized or not, perhaps we should also fix this.

from sktime.

Ah, thanks for the clarification. I forgot the i-1 terms.

Would you like to make a pull request with a fix?

from sktime.

I don't think z-scoring the time series in input is mandatory.

Yes, of course - my issue is that it is not actually clear whether it is done or not, to a user.

from sktime.