ENH: new feature table type for euclidean continuous feature values

[VinzentRisch]

Improvement Description
I propose introducing a new semantic type FeatureTable[Unconstrained] to represent feature tables that represent euclidean continuous feature values. This includes data transformed from compositional (Aitchison simplex) to Euclidean space, e.g. via CLR transformation of FeatureTable[Frequency].

CLR-transformed metagenomics data are required for methods that assume Euclidean geometry (e.g. PCA, MFA). Currently, there is no semantic type that explicitly represents this state.

FeatureTable[Unconstrained] could also be used for metabolomics data because intensity tables also represent Euclidean continuous feature values.

[VinzentRisch]

Hey @ebolyen

I am still thinking about this. The term continuous seems ambiguous for what we want to describe. Because continuous does not always mean euclidian. For instance, TPM normalization produces real-valued (continuous) data, but the resulting table is still constrained by compositional effects and therefore not euclidean.

Do you think this is a problem? Should we go with an option that is less ambiguous?

[ebolyen]

FeatureTable[Unconstrained]? You are right that this is an issue with the simplex and realistically any constrained topology (unit-sphere or other, weirder things). What we want is for the data to be unconstrained, so maybe we just say that? What do you think?

[ebolyen]

[VinzentRisch]

I think that is better than continuous.
I also wanted to ask what you think about how the metabolomics data should be imported. Because it is not strictly compositional so it is also unconstrained. So what do you think of then importing the metabolomics data also as unconstrained?