"""Distances based on various backends."""
# Author: Hugues Van Assel <vanasselhugues@gmail.com>
#
# License: BSD 3-Clause License
import torch
from typing import Optional
from .torch import pairwise_distances_torch
from .keops import pairwise_distances_keops
from .faiss import pairwise_distances_faiss
[docs]
def pairwise_distances(
X: torch.Tensor,
Y: Optional[torch.Tensor] = None,
metric: str = "euclidean",
backend: Optional[str] = None,
exclude_diag: bool = False,
k: Optional[int] = None,
return_indices: bool = False,
):
r"""Compute pairwise distances between two tensors.
Parameters
----------
X : torch.Tensor of shape (n_samples, n_features)
Input data.
Y : torch.Tensor of shape (m_samples, n_features), optional
Input data. If None, Y is set to X.
metric : str, optional
Metric to use. Default is "euclidean".
backend : {'keops', 'faiss', None}, optional
Backend to use for computation.
If None, use standard torch operations.
exclude_diag : bool, optional
Whether to exclude the diagonal from the distance matrix.
Only used when k is not None. Default is False.
k : int, optional
If not None, return only the k-nearest neighbors.
return_indices : bool, optional
Whether to return the indices of the k-nearest neighbors.
Default is False.
Returns
-------
C : torch.Tensor
Pairwise distances.
indices : torch.Tensor, optional
Indices of the k-nearest neighbors. Only returned if k is not None.
"""
if backend == "keops":
C, indices = pairwise_distances_keops(
X=X, Y=Y, metric=metric, exclude_diag=exclude_diag, k=k
)
elif backend == "faiss":
if k is not None:
C, indices = pairwise_distances_faiss(
X=X, Y=Y, metric=metric, k=k, exclude_diag=exclude_diag
)
else:
raise ValueError(
"[TorchDR] ERROR : k must be provided when using `backend=faiss`."
)
else:
C, indices = pairwise_distances_torch(
X=X, Y=Y, metric=metric, k=k, exclude_diag=exclude_diag
)
if return_indices:
return C, indices
else:
return C
def symmetric_pairwise_distances_indices(
X: torch.Tensor,
indices: torch.Tensor,
metric: str = "sqeuclidean",
return_indices: bool = False,
):
r"""Compute pairwise distances for a subset of pairs given by indices.
The output distance matrix has shape (n, k) and its (i,j) element is the
distance between X[i] and Y[indices[i, j]].
Parameters
----------
X : torch.Tensor of shape (n, p)
Input dataset.
indices : torch.Tensor of shape (n, k)
Indices of the pairs for which to compute the distances.
metric : str, optional
Metric to use for computing distances. The default is "sqeuclidean".
return_indices : bool, optional
Whether to return the indices of the pairs for which to compute the distances.
Default is False.
Returns
-------
C_indices : torch.Tensor of shape (n, k)
Pairwise distances matrix for the subset of pairs.
indices : torch.Tensor of shape (n, k)
Indices of the pairs for which to compute the distances.
"""
X_indices = X[indices.int()] # Shape (n, k, p)
if metric == "sqeuclidean":
C_indices = torch.sum((X.unsqueeze(1) - X_indices) ** 2, dim=-1)
elif metric == "euclidean":
C_indices = torch.sum((X.unsqueeze(1) - X_indices) ** 2, dim=-1).sqrt()
elif metric == "manhattan":
C_indices = torch.sum(torch.abs(X.unsqueeze(1) - X_indices), dim=-1)
elif metric == "angular":
C_indices = -torch.sum(X.unsqueeze(1) * X_indices, dim=-1)
elif metric == "sqhyperbolic":
X_indices_norm = (X_indices**2).sum(-1)
X_norm = (X**2).sum(-1)
C_indices = torch.relu(torch.sum((X.unsqueeze(1) - X_indices) ** 2, dim=-1))
denom = (1 - X_norm).unsqueeze(-1) * (1 - X_indices_norm)
C_indices = torch.arccosh(1 + 2 * (C_indices / denom) + 1e-8) ** 2
else:
raise NotImplementedError(f"Metric '{metric}' is not (yet) implemented.")
if return_indices:
return C_indices, indices
else:
return C_indices
