Data processing wishlist

[odunbar]

We have

• data normalization in inputs
• truncated PCA
• individual dimension Standardization in outputs
• ParameterDistributions that can be GaussianRandomFields (on cube-type fixed discretization domains)

I find more and more a key issue is dealing with other data deficiencies (scalings, dimensionality etc) in general problems. Maybe it would be good to catalogue a wishlist of some other tools that might be worth looking at for messier data in future

• Correlation-based vs Covariance-based processing (maybe an indicator/automatic selection)
• Diffusion maps? (e.g. https://docs.juliahub.com/ManifoldLearning/Uw8bd/0.9.0/)
• Nonlinear PCA (e.g. kernel PCA, or random feature PCA https://arxiv.org/pdf/1706.06296.pdf)
• Graph-Manifold projections with say, UMAP.jl
• Summary of methods, in particular CCA https://www.cs.cmu.edu/~tom/10701_sp11/recitations/Recitation_11.pdf
• derivative free likelihood informed subspaces https://www.arxiv.org/abs/2410.19990

[odunbar]

#362
Linear options being addressed here. (e.g. normalization, CCA, derivative free LIS)