Climate novelty functions

[tpoisot]

Minimum version:

• in/out of range
• Euclidean distance
• Mesgaran type I/II
• PCA + distance

Best guess about interface:

novelty(EuclideanNovelty, baseline, projection)::SDMLayer

1. method (with optional distance to limit the radius)
2. vector of baseline
3. vector of preojections

[gottacatchenall]

PCA + distance

re this --- for computing velocity for the BONs.jl casestudy, I was planning on using whitening, but because there is always colinearity in the BioClim variables, this requires doing vif on them and removing the highest vif until the covariance matrix is positive-definite, which is kind of a pain. It also ignores the issue that in the future, variables with high baseline colinearity may not preserve it, so the dropped variables may actually contribute to non-redundant climate velocity in the future

Would PCA -> ZScore be a justifiable alternative? (It seems like unit variance across all variables would be important)

[tpoisot]

I think ultimately the PCA + distance is just a generic case of distance, where you PCA things first, and it would make sense that distance does z-score first by default - I haven't really thought about the interface yet anyway

[tpoisot]

A question that's been slowly rotating in my mind is: if you want to calculate novelty, you probably want to do that based on information that's related to the model you've trained on the baseline data. So maybe a nice way to approach this is to explicitly call the model when measuring novelty.

For example, you do a PCA + whatever, then you probably want to look at novelty in the space where you're making predictions, which means using only the selected variables + transformation. This can be done pretty quickly by adding an additional method to SDT that takes layers, and projects them using the transformer(sdm), and returning this as layers.

@gottacatchenall - would this solve your projection issue?

[gottacatchenall]

I think it would in SDM contexts --- although in the context of BONs.jl there is no model so in principle it should work for any combination of input layers. Does that make sense?

[tpoisot]

It does, good point. I'll think about this some more.