[ENH] Implement Minimal Variance Matching (MVM) distance function

[TonyBagnall]

Describe the feature or idea you want to propose

I found an elastic distance measure from the UCR group referenced in the MSM paper that I was not previously aware of.

L. Latecki, V. Megalooikonomou, Q. Wang, R. Laka¨mper, C. Ratanamahatana, and E. Keogh, “Elastic Partial Matching of Time
Series,” Proc. European Conf. Principles of Data Mining and Knowledge Discovery (PKDD)

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.79.5842&rep=rep1&type=pdf

referenced here
https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6189346

Describe your proposed solution

It would nice to have it in sktime implemented it as a numba distance in the module distances.

Describe alternatives you've considered, if relevant

No response

Additional context

No response

[tanishy7777]

Describe the feature or idea you want to propose

I found an elastic distance measure from the UCR group referenced in the MSM paper that I was not previously aware of.

L. Latecki, V. Megalooikonomou, Q. Wang, R. Laka¨mper, C. Ratanamahatana, and E. Keogh, “Elastic Partial Matching of Time Series,” Proc. European Conf. Principles of Data Mining and Knowledge Discovery (PKDD)

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.79.5842&rep=rep1&type=pdf

referenced here https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6189346

Describe your proposed solution

It would nice to have it in sktime implemented it as a numba distance in the module distances.

Describe alternatives you've considered, if relevant

No response

Additional context

No response

Hey, I would love to work on this. Can I assign this to myself?

[tanishy7777]

@aeon-actions-bot assign @tanishy7777

[tanishy7777]

I went through the paper https://www.researchgate.net/publication/220765855_Partial_Elastic_Matching_of_Time_Series and I have implemented a very primitive version of the algorithm but I had a small doubt from the paper. Could anyone please help me with the same?

Question: Bounds of the column indices
They have mentioned that after we convert the cost matrix to a DAG the starting node will be with row=1 and column will be 1<=j<=n − m and the path can end with column j = n−m, ..., n and row=m
but shouldn't the start node have column, 1 to n-m+1 and end node have column m to n instead?

I have attached a diagram illustrating the same.