Do we have a priori knowledge of Y in Gn = (V, E, Y) in the sample space

[yaxigeigei]

As the title. In addition, if we do know the category label Y, would it be easier to calculate l in loss function since we know both yi and yi_hat.

[yaxigeigei]

What if we don't?

[DSP137]

If I remember correctly, if Y is a latent feature, we know the possible values for Y, but we don't know which value each node takes on. For example, we might know that for any vertex, Y could be any number 1, 2, or 3 (Y = {1,2,3}), but for a particular vertex $v_i$, we don't know which value $y_i$ it actually has. As for the $\hat{y_i}$, I think it is an estimate for what we estimate $y$ is based on the sample we got.

[SandyaS72]

I think in this case, Y is referring to a label on a graph that indicates what "cluster" it is supposed to belong to. It's the 'ground truth" to check the clustering you get against to see how "good" your clustering was. If you don't know graph labels, I guess you could use some other method like checking the distance between points within clusters against the distance between points between clusters, for example. I'm a little confused about what you mean when you say "calculate I in loss function"....