chore: import upstream snapshot with attribution
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wehub-resource-sync
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"""Tensorflow Module for Chebyshev Spectral Graph Convolution layer"""
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# pylint: disable= no-member, arguments-differ, invalid-name
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import numpy as np
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import tensorflow as tf
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from tensorflow.keras import layers
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from .... import broadcast_nodes, function as fn
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from ....base import dgl_warning
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class ChebConv(layers.Layer):
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r"""Chebyshev Spectral Graph Convolution layer from `Convolutional
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Neural Networks on Graphs with Fast Localized Spectral Filtering
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<https://arxiv.org/pdf/1606.09375.pdf>`__
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.. math::
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h_i^{l+1} &= \sum_{k=0}^{K-1} W^{k, l}z_i^{k, l}
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Z^{0, l} &= H^{l}
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Z^{1, l} &= \tilde{L} \cdot H^{l}
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Z^{k, l} &= 2 \cdot \tilde{L} \cdot Z^{k-1, l} - Z^{k-2, l}
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\tilde{L} &= 2\left(I - \tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2}\right)/\lambda_{max} - I
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where :math:`\tilde{A}` is :math:`A` + :math:`I`, :math:`W` is learnable weight.
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Parameters
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----------
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in_feats: int
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Dimension of input features; i.e, the number of dimensions of :math:`h_i^{(l)}`.
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out_feats: int
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Dimension of output features :math:`h_i^{(l+1)}`.
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k : int
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Chebyshev filter size :math:`K`.
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activation : function, optional
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Activation function. Default ``ReLu``.
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bias : bool, optional
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If True, adds a learnable bias to the output. Default: ``True``.
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Example
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-------
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>>> import dgl
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>>> import numpy as np
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>>> import tensorflow as tf
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>>> from dgl.nn import ChebConv
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>>> with tf.device("CPU:0"):
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... g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
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... feat = tf.ones((6, 10))
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... conv = ChebConv(10, 2, 2)
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... res = conv(g, feat)
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... res
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<tf.Tensor: shape=(6, 2), dtype=float32, numpy=
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array([[ 0.6163, -0.1809],
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[ 0.6163, -0.1809],
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[ 0.6163, -0.1809],
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[ 0.9698, -1.5053],
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[ 0.3664, 0.7556],
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[-0.2370, 3.0164]], dtype=float32)>
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"""
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def __init__(
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self, in_feats, out_feats, k, activation=tf.nn.relu, bias=True
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):
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super(ChebConv, self).__init__()
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self._k = k
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self._in_feats = in_feats
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self._out_feats = out_feats
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self.activation = activation
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self.linear = layers.Dense(out_feats, use_bias=bias)
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def call(self, graph, feat, lambda_max=None):
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r"""Compute ChebNet layer.
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Parameters
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----------
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graph : DGLGraph
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The graph.
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feat : tf.Tensor
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The input feature of shape :math:`(N, D_{in})` where :math:`D_{in}`
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is size of input feature, :math:`N` is the number of nodes.
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lambda_max : list or tensor or None, optional.
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A list(tensor) with length :math:`B`, stores the largest eigenvalue
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of the normalized laplacian of each individual graph in ``graph``,
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where :math:`B` is the batch size of the input graph. Default: None.
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If None, this method would set the default value to 2.
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One can use :func:`dgl.laplacian_lambda_max` to compute this value.
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Returns
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-------
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tf.Tensor
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The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
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is size of output feature.
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"""
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def unnLaplacian(feat, D_invsqrt, graph):
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"""Operation Feat * D^-1/2 A D^-1/2"""
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graph.ndata["h"] = feat * D_invsqrt
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graph.update_all(fn.copy_u("h", "m"), fn.sum("m", "h"))
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return graph.ndata.pop("h") * D_invsqrt
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with graph.local_scope():
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in_degrees = tf.clip_by_value(
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tf.cast(graph.in_degrees(), tf.float32),
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clip_value_min=1,
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clip_value_max=np.inf,
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)
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D_invsqrt = tf.expand_dims(tf.pow(in_degrees, -0.5), axis=-1)
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if lambda_max is None:
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dgl_warning(
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"lambda_max is not provided, using default value of 2. "
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"Please use dgl.laplacian_lambda_max to compute the eigenvalues."
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)
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lambda_max = [2] * graph.batch_size
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if isinstance(lambda_max, list):
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lambda_max = tf.constant(lambda_max, dtype=tf.float32)
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if lambda_max.ndim == 1:
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lambda_max = tf.expand_dims(
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lambda_max, axis=-1
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) # (B,) to (B, 1)
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# broadcast from (B, 1) to (N, 1)
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lambda_max = broadcast_nodes(graph, lambda_max)
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re_norm = 2.0 / lambda_max
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# X_0 is the raw feature, Xt is the list of X_0, X_1, ... X_t
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X_0 = feat
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Xt = [X_0]
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# X_1(f)
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if self._k > 1:
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h = unnLaplacian(X_0, D_invsqrt, graph)
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X_1 = -re_norm * h + X_0 * (re_norm - 1)
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# Append X_1 to Xt
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Xt.append(X_1)
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# Xi(x), i = 2...k
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for _ in range(2, self._k):
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h = unnLaplacian(X_1, D_invsqrt, graph)
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X_i = -2 * re_norm * h + X_1 * 2 * (re_norm - 1) - X_0
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# Append X_i to Xt
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Xt.append(X_i)
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X_1, X_0 = X_i, X_1
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# Create the concatenation
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Xt = tf.concat(Xt, 1)
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# linear projection
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h = self.linear(Xt)
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# activation
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if self.activation:
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h = self.activation(h)
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return h
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