# Copyright 2022 Huawei Technologies Co., Ltd
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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# ============================================================================
"""GMMConv Layer"""
import math
import mindspore as ms
from mindspore.common.initializer import XavierUniform
from mindspore_gl import Graph
from .. import GNNCell
[文档]class GMMConv(GNNCell):
r"""
Gaussian mixture model convolutional layer.
From the paper `Geometric Deep Learning on Graphs and Manifolds using Mixture Model CNNs <http://openaccess.thecvf.com/content_cvpr_2017/papers/Monti_Geometric_Deep_Learning_CVPR_2017_paper.pdf>`_ .
.. math::
u_{ij} = f(x_i, x_j), x_j \in \mathcal{N}(i) \\
w_k(u) = \exp\left(-\frac{1}{2}(u-\mu_k)^T \Sigma_k^{-1} (u - \mu_k)\right) \\
h_i^{l+1} = \mathrm{aggregate}\left(\left\{\frac{1}{K}
\sum_{k}^{K} w_k(u_{ij}), \forall j\in \mathcal{N}(i)\right\}\right)
where :math:`u` represents the pseudo coordinate between the vertex and one of its neighbors, computed using the
function :math:`f`, where :math:`\Sigma_k^{-1}` and :math:`\mu_k` are the learnable parameters of the covariance
matrix and the mean vector of the Gaussian kernel.
Args:
in_feat_size (int): Input node feature size.
out_feat_size (int): Output node feature size.
coord_dim (int): Dimension of pseudo-coordinates.
n_kernels (int): Number of kernels.
residual (bool, optional): Whether use residual. Default: ``False``.
bias (bool, optional): Whether use bias. Default: ``False``.
aggregator_type (str, optional): Type of aggregator, should be ``'sum'``. Default: ``'sum'``.
Inputs:
- **x** (Tensor) - The input node features. The shape is :math:`(N, D_{in})`
where :math:`N` is the number of nodes,
and :math:`D_{in}` should be equal to `in_feat_size` in `Args`.
- **pseudo** (Tensor) - Pseudo coordinate tensor.
- **g** (Graph) - The input graph.
Outputs:
- Tensor, output node features with shape of :math:`(N, D_{out})`, where :math:`(D_{out})` should be the same as
`out_size` in `Args`.
Raises:
SyntaxError: when the aggregator type not equals to ``'sum'``.
TypeError: If `in_feat_size` or `out_feat_size` or `coord_dim` or `n_kernels` is not an int.
TypeError: If `bias` or `residual` is not a bool.
Supported Platforms:
``Ascend`` ``GPU``
Examples:
>>> import mindspore as ms
>>> from mindspore_gl.nn import GMMConv
>>> from mindspore_gl import GraphField
>>> n_nodes = 4
>>> n_edges = 7
>>> node_feat_size = 7
>>> src_idx = ms.Tensor([0, 1, 1, 2, 2, 3, 3], ms.int32)
>>> dst_idx = ms.Tensor([0, 0, 2, 1, 3, 0, 1], ms.int32)
>>> ones = ms.ops.Ones()
>>> node_feat = ones((n_nodes, node_feat_size), ms.float32)
>>> graph_field = GraphField(src_idx, dst_idx, n_nodes, n_edges)
>>> meanconv = GMMConv(in_feat_size=node_feat_size, out_feat_size=2, coord_dim=3, n_kernels=2)
>>> pseudo = ones((7, 3), ms.float32)
>>> res = meanconv(node_feat, pseudo, *graph_field.get_graph())
>>> print(res.shape)
(4, 2)
"""
def __init__(self,
in_feat_size: int,
out_feat_size: int,
coord_dim: int,
n_kernels: int,
residual=False,
bias=False,
aggregator_type="sum"):
super().__init__()
if (not isinstance(in_feat_size, int)) or in_feat_size <= 0:
raise ValueError("in_feat_size must be positive int")
if (not isinstance(out_feat_size, int)) or out_feat_size <= 0:
raise ValueError("out_feat_size must be positive int")
if (not isinstance(coord_dim, int)) or coord_dim <= 0:
raise ValueError("coord_dim must be positive int")
if (not isinstance(n_kernels, int)) or n_kernels <= 0:
raise ValueError("n_kernels must be positive int")
if not isinstance(bias, bool):
raise ValueError("bias must be bool")
if not isinstance(residual, bool):
raise ValueError("residual must be bool")
if aggregator_type != "sum":
raise TypeError("Don't support aggregator type other than sum.")
self.mu = ms.Parameter(
ms.ops.normal((n_kernels, coord_dim), ms.Tensor([[0. for _ in range(coord_dim)]], ms.float32),
ms.Tensor([[0.1 for _ in range(coord_dim)]], ms.float32)))
self.inv_sigma = ms.Parameter(ms.ops.Ones()((n_kernels, coord_dim), ms.float32))
gain = math.sqrt(2)
self.dense = ms.nn.Dense(in_feat_size, out_feat_size * n_kernels, has_bias=bias,
weight_init=XavierUniform(gain))
self.residual = None
if residual:
self.residual = ms.nn.Dense(in_feat_size, out_feat_size, has_bias=bias, weight_init=XavierUniform(gain))
self.agg_type = aggregator_type
self.n_kernels = n_kernels
self.out_feat_size = out_feat_size
self.coord_dim = coord_dim
# pylint: disable=arguments-differ
def construct(self, x, pseudo, g: Graph):
"""
Construct function for GMMConv.
"""
g.set_vertex_attr({"h": ms.ops.Reshape()(self.dense(x), (-1, self.n_kernels, self.out_feat_size))})
gaussian = -0.5 * ((ms.ops.Reshape()(pseudo, (-1, 1, self.coord_dim)) - ms.ops.Reshape()(self.mu, (
1, self.n_kernels, self.coord_dim))) ** 2)
gaussian = gaussian * (ms.ops.Reshape()(self.inv_sigma, (1, self.n_kernels, self.coord_dim)) ** 2)
gaussian = ms.ops.Exp()(ms.ops.ReduceSum(keep_dims=True)(gaussian, -1))
g.set_edge_attr({"g": gaussian})
for v in g.dst_vertex:
e = [s.h * e.g for s, e in v.inedges]
v.rt = g.sum(e)
v.rt = ms.ops.ReduceSum()(v.rt, 1)
if self.residual is not None:
v.rt = v.rt + self.residual(v.h)
return [v.rt for v in g.dst_vertex]