import torch
from torch import Tensor
[docs]def approx_knn(
x: Tensor,
y: Tensor,
k: int,
batch_x: Tensor = None,
batch_y: Tensor = None,
) -> Tensor: # pragma: no cover
r"""Finds for each element in :obj:`y` the :obj:`k` approximated nearest
points in :obj:`x`.
.. note::
Approximated :math:`k`-nearest neighbor search is performed via the
`pynndescent <https://pynndescent.readthedocs.io/en/latest>`_ library.
Args:
x (torch.Tensor): Node feature matrix
:math:`\mathbf{X} \in \mathbb{R}^{N \times F}`.
y (torch.Tensor): Node feature matrix
:math:`\mathbf{X} \in \mathbb{R}^{M \times F}`.
k (int): The number of neighbors.
batch_x (torch.Tensor, optional): Batch vector
:math:`\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N`, which assigns each
node to a specific example. (default: :obj:`None`)
batch_y (torch.Tensor, optional): Batch vector
:math:`\mathbf{b} \in {\{ 0, \ldots, B-1\}}^M`, which assigns each
node to a specific example. (default: :obj:`None`)
:rtype: :class:`torch.Tensor`
"""
from pynndescent import NNDescent
if batch_x is None:
batch_x = x.new_zeros(x.size(0), dtype=torch.long)
if batch_y is None:
batch_y = y.new_zeros(y.size(0), dtype=torch.long)
x = x.view(-1, 1) if x.dim() == 1 else x
y = y.view(-1, 1) if y.dim() == 1 else y
assert x.dim() == 2 and batch_x.dim() == 1
assert y.dim() == 2 and batch_y.dim() == 1
assert x.size(1) == y.size(1)
assert x.size(0) == batch_x.size(0)
assert y.size(0) == batch_y.size(0)
min_xy = min(x.min(), y.min())
x, y = x - min_xy, y - min_xy
max_xy = max(x.max(), y.max())
x, y, = x / max_xy, y / max_xy
# Concat batch/features to ensure no cross-links between examples exist:
x = torch.cat([x, 2 * x.size(1) * batch_x.view(-1, 1).to(x.dtype)], dim=-1)
y = torch.cat([y, 2 * y.size(1) * batch_y.view(-1, 1).to(y.dtype)], dim=-1)
index = NNDescent(x.detach().cpu().numpy())
col, dist = index.query(y.detach().cpu().numpy(), k=k)
dist = torch.from_numpy(dist).view(-1).to(x.device, x.dtype)
col = torch.from_numpy(col).view(-1).to(x.device, torch.long)
row = torch.arange(y.size(0), device=x.device, dtype=torch.long)
row = row.repeat_interleave(k)
mask = ~torch.isinf(dist)
row, col = row[mask], col[mask]
return torch.stack([row, col], dim=0)
[docs]def approx_knn_graph(
x: Tensor,
k: int,
batch: Tensor = None,
loop: bool = False,
flow: str = 'source_to_target',
) -> Tensor: # pragma: no cover
r"""Computes graph edges to the nearest approximated :obj:`k` points.
.. note::
Approximated :math:`k`-nearest neighbor search is performed via the
`pynndescent <https://pynndescent.readthedocs.io/en/latest>`_ library.
Args:
x (torch.Tensor): Node feature matrix
:math:`\mathbf{X} \in \mathbb{R}^{N \times F}`.
k (int): The number of neighbors.
batch (torch.Tensor, optional): Batch vector
:math:`\mathbf{b} \in {\{ 0, \ldots, B-1\}}^N`, which assigns each
node to a specific example. (default: :obj:`None`)
loop (bool, optional): If :obj:`True`, the graph will contain
self-loops. (default: :obj:`False`)
flow (str, optional): The flow direction when using in combination with
message passing (:obj:`"source_to_target"` or
:obj:`"target_to_source"`). (default: :obj:`"source_to_target"`)
:rtype: :class:`torch.Tensor`
"""
assert flow in ['source_to_target', 'target_to_source']
row, col = approx_knn(x, x, k if loop else k + 1, batch, batch)
row, col = (col, row) if flow == 'source_to_target' else (row, col)
if not loop:
mask = row != col
row, col = row[mask], col[mask]
return torch.stack([row, col], dim=0)