[ENH] Allow KMeans and KMedoids to work with unequal length series

[TonyBagnall]

Describe the feature or idea you want to propose

these two should be easy to adapt for unequal length, see #408

Describe your proposed solution

swap shape[0] for len

Describe alternatives you've considered, if relevant

No response

Additional context

No response

[TonyBagnall]

@chrisholder bumping this as it should be easy to do, with usual numpy disclaimers

[TonyBagnall]

discussed 25/10 at module meeting. there is an issue with how to find prototypes with unequal length, i.e. what length. This issue can now wait until the new module is ready

[hadifawaz1999]

Francois's paper, dba proposed an algorithm called Adaptive Scaling to find the best length of the average, from the conclusion of the paper "The length of the average sequence is not trivial to choose.
It has to be as short as possible, but also sufficiently long to
represent the data it covers. This article also introduces a short-
ening technique of the length of a sequence called Adaptive
Scaling. This process is shown to shorten the average sequence
in adequacy to DTW and to the data, but also to improve its
representativity."

[ron0studios]

Hi, I would like to contribute to this issue if it is available. I will be reading through the #408 implementation, although I may need some clarification on what was discussed on the 25/10 meeting. Let me know if this is possible, thanks!

[MatthewMiddlehurst]

Hi I don't think this is a good issue currently as I think @hadifawaz1999 and @chrisholder want to develop a prototyping module which would impact this. This also seems to have some element of research and is not just a code change.

[ron0studios]

Ah I see, thanks for letting me know!