For simplicity I am going start with a toy example first.
Lets suppose we have a set of
Y in the space, distributed with the shape of the letter M and you want to fit those using 4 lines. These points are not ordered in the sense that the order of the points in the vector
Y is shuffled.
So I built a my function
f that given 5 points
P, it generates 4 lines concatenated joining those 5 points. I want to find the 5 points
P that I can use to best describe the data. This is, the lines are close to the points.
So basically my though here is, given values
x in [0,1] and my function
f(x, P) I can sample points from this function and compute the loss against the
Loss(f(x,P), Y). For example if x is
torch.linspace(0, 1, 100) I am gong to draw 100 points from my function. I can also draw
n points. Whatever it works.
If the points of the ground truth would be ordered and kind of evenly distributed I can use the
MSELoss function and I can get the 5 points (I already tried this and it works). However if the
Y points are unordered this loss is no longer working.
My question is then, which kind of loss function I can use here to find
My problem is a little bit more general and I have a set of points
Y that follow a line that curves through the 3d space so I would like to use m concatenated lines given by
f(P}) whose distribution best matches