Add Tsallis metric

[gallardoalba]

Tsallis entropy is a generalization of the classical Shannon entropy, introducing a parameter q that adjusts the sensitivity of the entropy measure to the distribution of probabilities. For q = 1 Tsallis entropy reduces to Shannon entropy. For q != 1 it allows more or less emphasis on rare or abundant events in the data.

Source: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0266618

Addition of Tsallis entropy metric:

• The Tsallis entropy metric was implemented as a new diversity measure, allowing users to specify the parameter q.
• Functions and documentation were updated to support Tsallis entropy, including the ability to calculate it for a range of q values.
• The vignette and examples were expanded to demonstrate the use and interpretation of Tsallis entropy in splicing diversity analysis.

[gallardoalba]

I am not really sure if the linear model test should be included as a new function, or just keep is as an usage example in the vignette.

[gallardoalba]

Dear Dr. @esebesty, I think the code is ready for review. My intention is to integrate this tool in this Galaxy training https://training.galaxyproject.org/training-material/topics/transcriptomics/tutorials/differential-isoform-expression/tutorial.html

[gallardoalba]

Dear @esebesty, finally I decided to create an independen package for integrating the Tsallis analyis (TSENAT). I used theSplicingFactory code as reference, but modified it substantially; I mentioned that in the README. I hope this is fine for you. I think it is a better approach, since I would be interested in keeping expanding the Tsallis analyisis, and it would make it much easier. Please, feel free to contribute or provide feedback, it would be very welcome. Thank you so much in any case.

[esebesty]

Hey, sorry for the delay, stuff happened, and had no time, I can merge your pull request now, if you are still planning it.

[gallardoalba]

Yes, the PR can be merged if you find it adequate, but first I would like to improve the implementation.

[esebesty]

OK, great, I'll wait for your improved implementation. In the meantime, I'll update the build workflow config.

[gallardoalba]

Hi @esebesty, the improvements where included, sorry for the delay.

[gallardoalba]

I modified the implementation because the tests (Wilcoxon/Shuffle) are not adequate for Tsallis multi-q values. Also the implementation has been enhanced for using natural logarithm base for mathematical rigor, species richness support (q=0), vectorized matrix operations for efficiency, and numerical stability (q_tol=1e-6). I made deep research on Tsallis entropy on the last months; the results are summarized in https://gallardoalba.github.io/TSENAT/articles/TSENAT.html. Regards.

[gallardoalba]

The work on Tsallis entropy is not published (I developed this small project on it in my free time); if you are interested in working on it with me, let me know; I am very interesting in the entropy-based approach @esebesty.