Source code for dgl.nn.pytorch.factory

"""Modules that transforms between graphs and between graph and tensors."""
import torch.nn as nn

from ...transforms import knn_graph, radius_graph, segmented_knn_graph


def pairwise_squared_distance(x):
    """
    x : (n_samples, n_points, dims)
    return : (n_samples, n_points, n_points)
    """
    x2s = (x * x).sum(-1, keepdim=True)
    return x2s + x2s.transpose(-1, -2) - 2 * x @ x.transpose(-1, -2)


[docs]class KNNGraph(nn.Module): r"""Layer that transforms one point set into a graph, or a batch of point sets with the same number of points into a batched union of those graphs. The KNNGraph is implemented in the following steps: 1. Compute an NxN matrix of pairwise distance for all points. 2. Pick the k points with the smallest distance for each point as their k-nearest neighbors. 3. Construct a graph with edges to each point as a node from its k-nearest neighbors. The overall computational complexity is :math:`O(N^2(logN + D)`. If a batch of point sets is provided, the point :math:`j` in point set :math:`i` is mapped to graph node ID: :math:`i \times M + j`, where :math:`M` is the number of nodes in each point set. The predecessors of each node are the k-nearest neighbors of the corresponding point. Parameters ---------- k : int The number of neighbors. Notes ----- The nearest neighbors found for a node include the node itself. Examples -------- The following example uses PyTorch backend. >>> import torch >>> from dgl.nn.pytorch.factory import KNNGraph >>> >>> kg = KNNGraph(2) >>> x = torch.tensor([[0,1], [1,2], [1,3], [100, 101], [101, 102], [50, 50]]) >>> g = kg(x) >>> print(g.edges()) (tensor([0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5]), tensor([0, 0, 1, 2, 1, 2, 5, 3, 4, 3, 4, 5])) """ def __init__(self, k): super(KNNGraph, self).__init__() self.k = k # pylint: disable=invalid-name
[docs] def forward( self, x, algorithm="bruteforce-blas", dist="euclidean", exclude_self=False, ): r""" Forward computation. Parameters ---------- x : Tensor :math:`(M, D)` or :math:`(N, M, D)` where :math:`N` means the number of point sets, :math:`M` means the number of points in each point set, and :math:`D` means the size of features. algorithm : str, optional Algorithm used to compute the k-nearest neighbors. * 'bruteforce-blas' will first compute the distance matrix using BLAS matrix multiplication operation provided by backend frameworks. Then use topk algorithm to get k-nearest neighbors. This method is fast when the point set is small but has :math:`O(N^2)` memory complexity where :math:`N` is the number of points. * 'bruteforce' will compute distances pair by pair and directly select the k-nearest neighbors during distance computation. This method is slower than 'bruteforce-blas' but has less memory overhead (i.e., :math:`O(Nk)` where :math:`N` is the number of points, :math:`k` is the number of nearest neighbors per node) since we do not need to store all distances. * 'bruteforce-sharemem' (CUDA only) is similar to 'bruteforce' but use shared memory in CUDA devices for buffer. This method is faster than 'bruteforce' when the dimension of input points is not large. This method is only available on CUDA device. * 'kd-tree' will use the kd-tree algorithm (CPU only). This method is suitable for low-dimensional data (e.g. 3D point clouds) * 'nn-descent' is a approximate approach from paper `Efficient k-nearest neighbor graph construction for generic similarity measures <https://www.cs.princeton.edu/cass/papers/www11.pdf>`_. This method will search for nearest neighbor candidates in "neighbors' neighbors". (default: 'bruteforce-blas') dist : str, optional The distance metric used to compute distance between points. It can be the following metrics: * 'euclidean': Use Euclidean distance (L2 norm) :math:`\sqrt{\sum_{i} (x_{i} - y_{i})^{2}}`. * 'cosine': Use cosine distance. (default: 'euclidean') exclude_self : bool, optional If True, the output graph will not contain self loop edges, and each node will not be counted as one of its own k neighbors. If False, the output graph will contain self loop edges, and a node will be counted as one of its own k neighbors. Returns ------- DGLGraph A DGLGraph without features. """ return knn_graph( x, self.k, algorithm=algorithm, dist=dist, exclude_self=exclude_self )
[docs]class SegmentedKNNGraph(nn.Module): r"""Layer that transforms one point set into a graph, or a batch of point sets with different number of points into a batched union of those graphs. If a batch of point sets is provided, then the point :math:`j` in the point set :math:`i` is mapped to graph node ID: :math:`\sum_{p<i} |V_p| + j`, where :math:`|V_p|` means the number of points in the point set :math:`p`. The predecessors of each node are the k-nearest neighbors of the corresponding point. Parameters ---------- k : int The number of neighbors. Notes ----- The nearest neighbors found for a node include the node itself. Examples -------- The following example uses PyTorch backend. >>> import torch >>> from dgl.nn.pytorch.factory import SegmentedKNNGraph >>> >>> kg = SegmentedKNNGraph(2) >>> x = torch.tensor([[0,1], ... [1,2], ... [1,3], ... [100, 101], ... [101, 102], ... [50, 50], ... [24,25], ... [25,24]]) >>> g = kg(x, [3,3,2]) >>> print(g.edges()) (tensor([0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 7]), tensor([0, 0, 1, 2, 1, 2, 3, 4, 5, 3, 4, 5, 6, 7, 6, 7])) >>> """ def __init__(self, k): super(SegmentedKNNGraph, self).__init__() self.k = k # pylint: disable=invalid-name
[docs] def forward( self, x, segs, algorithm="bruteforce-blas", dist="euclidean", exclude_self=False, ): r"""Forward computation. Parameters ---------- x : Tensor :math:`(M, D)` where :math:`M` means the total number of points in all point sets, and :math:`D` means the size of features. segs : iterable of int :math:`(N)` integers where :math:`N` means the number of point sets. The number of elements must sum up to :math:`M`. And any :math:`N` should :math:`\ge k` algorithm : str, optional Algorithm used to compute the k-nearest neighbors. * 'bruteforce-blas' will first compute the distance matrix using BLAS matrix multiplication operation provided by backend frameworks. Then use topk algorithm to get k-nearest neighbors. This method is fast when the point set is small but has :math:`O(N^2)` memory complexity where :math:`N` is the number of points. * 'bruteforce' will compute distances pair by pair and directly select the k-nearest neighbors during distance computation. This method is slower than 'bruteforce-blas' but has less memory overhead (i.e., :math:`O(Nk)` where :math:`N` is the number of points, :math:`k` is the number of nearest neighbors per node) since we do not need to store all distances. * 'bruteforce-sharemem' (CUDA only) is similar to 'bruteforce' but use shared memory in CUDA devices for buffer. This method is faster than 'bruteforce' when the dimension of input points is not large. This method is only available on CUDA device. * 'kd-tree' will use the kd-tree algorithm (CPU only). This method is suitable for low-dimensional data (e.g. 3D point clouds) * 'nn-descent' is a approximate approach from paper `Efficient k-nearest neighbor graph construction for generic similarity measures <https://www.cs.princeton.edu/cass/papers/www11.pdf>`_. This method will search for nearest neighbor candidates in "neighbors' neighbors". (default: 'bruteforce-blas') dist : str, optional The distance metric used to compute distance between points. It can be the following metrics: * 'euclidean': Use Euclidean distance (L2 norm) :math:`\sqrt{\sum_{i} (x_{i} - y_{i})^{2}}`. * 'cosine': Use cosine distance. (default: 'euclidean') exclude_self : bool, optional If True, the output graph will not contain self loop edges, and each node will not be counted as one of its own k neighbors. If False, the output graph will contain self loop edges, and a node will be counted as one of its own k neighbors. Returns ------- DGLGraph A batched DGLGraph without features. """ return segmented_knn_graph( x, self.k, segs, algorithm=algorithm, dist=dist, exclude_self=exclude_self, )
[docs]class RadiusGraph(nn.Module): r"""Layer that transforms one point set into a bidirected graph with neighbors within given distance. The RadiusGraph is implemented in the following steps: 1. Compute an NxN matrix of pairwise distance for all points. 2. Pick the points within distance to each point as their neighbors. 3. Construct a graph with edges to each point as a node from its neighbors. The nodes of the returned graph correspond to the points, where the neighbors of each point are within given distance. Parameters ---------- r : float Radius of the neighbors. p : float, optional Power parameter for the Minkowski metric. When :attr:`p = 1` it is the equivalent of Manhattan distance (L1 norm) and Euclidean distance (L2 norm) for :attr:`p = 2`. (default: 2) self_loop : bool, optional Whether the radius graph will contain self-loops. (default: False) compute_mode : str, optional ``use_mm_for_euclid_dist_if_necessary`` - will use matrix multiplication approach to calculate euclidean distance (p = 2) if P > 25 or R > 25 ``use_mm_for_euclid_dist`` - will always use matrix multiplication approach to calculate euclidean distance (p = 2) ``donot_use_mm_for_euclid_dist`` - will never use matrix multiplication approach to calculate euclidean distance (p = 2). (default: donot_use_mm_for_euclid_dist) Examples -------- The following examples uses PyTorch backend. >>> import dgl >>> from dgl.nn.pytorch.factory import RadiusGraph >>> x = torch.tensor([[0.0, 0.0, 1.0], ... [1.0, 0.5, 0.5], ... [0.5, 0.2, 0.2], ... [0.3, 0.2, 0.4]]) >>> rg = RadiusGraph(0.75) >>> g = rg(x) # Each node has neighbors within 0.75 distance >>> g.edges() (tensor([0, 1, 2, 2, 3, 3]), tensor([3, 2, 1, 3, 0, 2])) When :attr:`get_distances` is True, forward pass returns the radius graph and distances for the corresponding edges. >>> x = torch.tensor([[0.0, 0.0, 1.0], ... [1.0, 0.5, 0.5], ... [0.5, 0.2, 0.2], ... [0.3, 0.2, 0.4]]) >>> rg = RadiusGraph(0.75) >>> g, dist = rg(x, get_distances=True) >>> g.edges() (tensor([0, 1, 2, 2, 3, 3]), tensor([3, 2, 1, 3, 0, 2])) >>> dist tensor([[0.7000], [0.6557], [0.6557], [0.2828], [0.7000], [0.2828]]) """ # pylint: disable=invalid-name def __init__( self, r, p=2, self_loop=False, compute_mode="donot_use_mm_for_euclid_dist", ): super(RadiusGraph, self).__init__() self.r = r self.p = p self.self_loop = self_loop self.compute_mode = compute_mode # pylint: disable=invalid-name
[docs] def forward(self, x, get_distances=False): r""" Forward computation. Parameters ---------- x : Tensor The point coordinates. :math:`(N, D)` where :math:`N` means the number of points in the point set, and :math:`D` means the size of the features. It can be either on CPU or GPU. Device of the point coordinates specifies device of the radius graph. get_distances : bool, optional Whether to return the distances for the corresponding edges in the radius graph. (default: False) Returns ------- DGLGraph The constructed graph. The node IDs are in the same order as :attr:`x`. torch.Tensor, optional The distances for the edges in the constructed graph. The distances are in the same order as edge IDs. """ return radius_graph( x, self.r, self.p, self.self_loop, self.compute_mode, get_distances )