skshapes.loss.lp.LandmarkLoss

class skshapes.loss.lp.LandmarkLoss(p=2)

Bases: BaseLoss

Landmark loss for PolyData.

This class defines the Lp loss between the landmarks of two PolyData objects. If $X=(x_i)$ and $Y=(y_i)$ are the landmarks of two PolyData objects, the Lp loss is defined as:

$$Lp(X,Y)=\sum _i\Vert x_i-y_i{\Vert }^{(p/2)}$$

X and Y must have the same number of landmarks. What is more, the landmarks must be in correspondence, i.e. $x_i$ and $y_i$ must correspond to the same landmark. If this is not the case, the loss will be meaningless, consider using a loss function based on Optimal Transport or Nearest Neighbors instead.

Parameters:

p (int | float) – the indice of the Lp Norm. Defaults to 2.

__init__(p=2)

Initialize the LandmarkLoss class.

Methods

__init__([p])

Initialize the LandmarkLoss class.