scipy.cluster.hierarchy.optimal_leaf_ordering should use newer algorithm from Bar-Joseph et al. 2001

[xplat]

The current algorithm is O(n^4) so borderline impractical even for moderately-sized problems.

In [BJ01] is described an O(n^3) algorithm for the same problem. Compared to the current algorithm, the list of authors overlaps considerably and it is actually only a slight variation. It should be practical for considerably larger problems and more in line with the time spent computing the actual clustering, so it should see a lot more use.

[BJ01] Bar-Joseph Z, Biedl T, Brejova B, Demaine E, Gifford D, Hamel A, Jaakola T, Srebro N, Vinar T: Optimal arrangement of leaves in the tree representing hierarchical clustering of gene expression data. In Tech Rep 14. Department of Computer Science, University of Waterloo; 2001.

[rgommers]

Thanks for the suggestion @xplat, sounds like a good idea to update the algorithm. Would you be interested in working on this? Or @jamestwebber maybe?

[jamestwebber]

It seems like a good idea. I will have to read the paper before knowing how hard it might be to implement...and it seems like that we'll need some tests to verify the results and prevent issues like #11227 from happening again. @xplat if you are willing to help test and review code that would be great.