[ENH] Distances cost functions: default to absolute?

[TonyBagnall]

Describe the feature or idea you want to propose

after discussions with authors of this paper

https://link.springer.com/article/10.1007/s10618-023-00926-8

the point was made that it might be better to make all distance functions default to the absolute pointwise difference rather than the squared value. We have consistently seen MSM outperform other distances at a range of tasks, and based on the findings of the above paper it is likely that at least some of this improvement comes from the absolute rather than squared value,

Describe your proposed solution

This would of course be a big change and not something to do lightly. It would be interesting to see if it makes a difference for clustering/classification/regression and if it is better, maybe make the change in a major release.

Describe alternatives you've considered, if relevant

No response

Additional context

No response

[MatthewMiddlehurst]

Would it be possible to parameterise this if its not already?

I think we have had this conversation before (probably multiple times), but it has slipped my mind so apologies 🙂.

[inclinedadarsh]

Parameterizing the cost functions as MSE and MAE sounds a very good option, however, as I'm a beginner I'll have to study more about it.

This sounds like a pretty good issue to get started as code contributions (as I have already gotten my hands dirty in documentation contributions)
Can I attempt it @TonyBagnall @MatthewMiddlehurst ?

[MatthewMiddlehurst]

I wouldn't personally if you are not familiar with the topic and code. A lot of changes to to complex numba code requiring some knowledge of the distances. Likely to require evaluation of the effects and may get bogged down in discussion. Elastic distance cost functions would not involve MSE or MAE.