Minkowski Distance

Functional Interface

torchmetrics.functional.pairwise_minkowski_distance(x, y=None, exponent=2, reduction=None, zero_diagonal=None)[source]

Calculate pairwise minkowski distances.

\[d_{minkowski}(x,y,p) = ||x - y||_p = \sqrt[p]{\sum_{d=1}^D (x_d - y_d)^p}\]

If both \(x\) and \(y\) are passed in, the calculation will be performed pairwise between the rows of \(x\) and \(y\). If only \(x\) is passed in, the calculation will be performed between the rows of \(x\).

  • x (Tensor) – Tensor with shape [N, d]

  • y (Optional[Tensor]) – Tensor with shape [M, d], optional

  • exponent (Union[int, float]) – int or float larger than 1, exponent to which the difference between preds and target is to be raised

  • reduction (Optional[Literal['mean', 'sum', 'none', None]]) – reduction to apply along the last dimension. Choose between ‘mean’, ‘sum’ (applied along column dimension) or ‘none’, None for no reduction

  • zero_diagonal (Optional[bool]) – if the diagonal of the distance matrix should be set to 0. If only x is given this defaults to True else if y is also given it defaults to False

Return type:



A [N,N] matrix of distances if only x is given, else a [N,M] matrix


>>> import torch
>>> from torchmetrics.functional.pairwise import pairwise_minkowski_distance
>>> x = torch.tensor([[2, 3], [3, 5], [5, 8]], dtype=torch.float32)
>>> y = torch.tensor([[1, 0], [2, 1]], dtype=torch.float32)
>>> pairwise_minkowski_distance(x, y, exponent=4)
tensor([[3.0092, 2.0000],
        [5.0317, 4.0039],
        [8.1222, 7.0583]])
>>> pairwise_minkowski_distance(x, exponent=4)
tensor([[0.0000, 2.0305, 5.1547],
        [2.0305, 0.0000, 3.1383],
        [5.1547, 3.1383, 0.0000]])