## Continuous ground truth in supervised (metric) learning?

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I am writing my thesis in the field of (deep) metric learning (DML). I am training a network in the fashion of contrastive / triplet Siamese networks to learn similarity and dissimilarity of inputs. In this context, the ground truth is commonly expressed as a binary. Let's take an example based on the similarity of species:

• Image A: german shepard (dog)
• Image B: siberian husky (dog)
• Image C: turkish angora (cat)
• Image D: gray wolf (wolf)

Image A and B are similar: same species, same sub-species (canis lupus) -> 1.0 == TRUE

Image A and C are dissimilar: different species (canis lupus vs. felis silvestris) -> 0.0 == FALSE

Image A and D ? same species, but different sub-species -> 0.8

Which metric learning approaches use a continuous ground truth for learning?

I could imagine that there is a lot of research out there using a continuous ground truth in classification settings. For instance to learn that the expression of a face is "almost (60%) happy", or more controversial, an image of a person depicts a "70% attractive person". Also in this fields I would be happy for hints / links.

Remarks:

• I don't ask for opinions on whether this makes sense or not.