[ENH] Implement Proximity Forest 2.0 classifier using aeon distances

[itsdivya1309]

Reference Issues/PRs

Closes: #428
Incorporates changes suggested in #1874 (maybe we can close PR #1876)

What does this implement/fix? Explain your changes.

1. Created a private distance file to parameterise DTW and ADTW distances.
2. Created a function to calculate the first_order_derivative of a time series.
3. Implemented the ProximityTree2 and ProximityForest2 class, as per the paper.
4. Added the classes to API.
5. Wrote unit tests.

To do:

• Improve the computational efficiency by implementing Early Abandoning and Pruning algorithm for elastic distance measures.

[aeon-actions-bot]

Thank you for contributing to aeon

I have added the following labels to this PR based on the title: [ $\color{#FEF1BE}{\textsf{enhancement}}$ ].
I have added the following labels to this PR based on the changes made: [ $\color{#BCAE15}{\textsf{classification}}$ ]. Feel free to change these if they do not properly represent the PR.

The Checks tab will show the status of our automated tests. You can click on individual test runs in the tab or "Details" in the panel below to see more information if there is a failure.

If our pre-commit code quality check fails, any trivial fixes will automatically be pushed to your PR unless it is a draft.

Don't hesitate to ask questions on the aeon Slack channel if you have any.

PR CI actions

These checkboxes will add labels to enable/disable CI functionality for this PR. This may not take effect immediately, and a new commit may be required to run the new configuration.

• Run pre-commit checks for all files
• Run all pytest tests and configurations
• Run all notebook example tests
• Run numba-disabled codecov tests
• Stop automatic pre-commit fixes (always disabled for drafts)
• Push an empty commit to re-run CI checks

[MatthewMiddlehurst]

I would put the distances in the same file as pf2 for now

[TonyBagnall]

have we compared results vs published?

[MatthewMiddlehurst]

Not yet, need to put it on the cluster. I have not got results for the original yet also.

[itsdivya1309]

have we compared results vs published?

Actually, the algorithm isn't complete yet. We still need to work on computational power, particularly integrating the EAP technique. I'd resume the work in a couple of days.

[MatthewMiddlehurst]

Want to run this soon. This is not blocking that, but some component seems to be non-deterministic.