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# Copyright 2019-2020 Data61, CSIRO
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import warnings
from tensorflow.keras.layers import Dense, Lambda, Dropout, Input, Layer
import tensorflow.keras.backend as K
from ..mapper import FullBatchGenerator
from .preprocessing_layer import GraphPreProcessingLayer
from .misc import SqueezedSparseConversion
[docs]class APPNPPropagationLayer(Layer):
"""
Implementation of Approximate Personalized Propagation of Neural Predictions (PPNP)
as in https://arxiv.org/abs/1810.05997.
Notes:
- The inputs are tensors with a batch dimension of 1:
Keras requires this batch dimension, and for full-batch methods
we only have a single "batch".
- There are three inputs required, the node features, the output
indices (the nodes that are to be selected in the final layer)
and the normalized graph Laplacian matrix
- This class assumes that the normalized Laplacian matrix is passed as
input to the Keras methods.
- The output indices are used when ``final_layer=True`` and the returned outputs
are the final-layer features for the nodes indexed by output indices.
- If ``final_layer=False`` all the node features are output in the same ordering as
given by the adjacency matrix.
Args:
units (int): dimensionality of output feature vectors
final_layer (bool): If False the layer returns output for all nodes,
if True it returns the subset specified by the indices passed to it.
teleport_probability: "probability" of returning to the starting node in the propogation step as desribed in
the paper (alpha in the paper)
"""
def __init__(self, units, teleport_probability=0.1, final_layer=False, **kwargs):
if "input_shape" not in kwargs and "input_dim" in kwargs:
kwargs["input_shape"] = (kwargs.get("input_dim"),)
super().__init__(**kwargs)
self.units = units
self.teleport_probability = teleport_probability
self.final_layer = final_layer
[docs] def get_config(self):
"""
Gets class configuration for Keras serialization.
Used by keras model serialization.
Returns:
A dictionary that contains the config of the layer
"""
config = {
"units": self.units,
"final_layer": self.final_layer,
"teleport_probability": self.teleport_probability,
}
base_config = super().get_config()
return {**base_config, **config}
[docs] def compute_output_shape(self, input_shapes):
"""
Computes the output shape of the layer.
Assumes the following inputs:
Args:
input_shapes (tuple of ints)
Shape tuples can include None for free dimensions, instead of an integer.
Returns:
An input shape tuple.
"""
feature_shape, out_shape, *As_shapes = input_shapes
batch_dim = feature_shape[0]
if self.final_layer:
out_dim = out_shape[1]
else:
out_dim = feature_shape[1]
return batch_dim, out_dim, self.units
[docs] def build(self, input_shapes):
"""
Builds the layer
Args:
input_shapes (list of int): shapes of the layer's inputs (node features and adjacency matrix)
"""
self.built = True
[docs] def call(self, inputs):
"""
Applies the layer.
Args:
inputs (list): a list of 3 input tensors that includes
propagated node features (size 1 x N x F),
node features (size 1 x N x F),
output indices (size 1 x M)
graph adjacency matrix (size N x N),
where N is the number of nodes in the graph, and
F is the dimensionality of node features.
Returns:
Keras Tensor that represents the output of the layer.
"""
propagated_features, features, out_indices, *As = inputs
batch_dim, n_nodes, _ = K.int_shape(features)
if batch_dim != 1:
raise ValueError(
"Currently full-batch methods only support a batch dimension of one"
)
# Remove singleton batch dimension
features = K.squeeze(features, 0)
propagated_features = K.squeeze(propagated_features, 0)
out_indices = K.squeeze(out_indices, 0)
# Propagate the node features
A = As[0]
output = (1 - self.teleport_probability) * K.dot(
A, propagated_features
) + self.teleport_probability * features
# On the final layer we gather the nodes referenced by the indices
if self.final_layer:
output = K.gather(output, out_indices)
# Add batch dimension back if we removed it
if batch_dim == 1:
output = K.expand_dims(output, 0)
return output
[docs]class APPNP:
"""
Implementation of Approximate Personalized Propagation of Neural Predictions (APPNP)
as in https://arxiv.org/abs/1810.05997.
The model minimally requires specification of the fully connected layer sizes as a list of ints
corresponding to the feature dimensions for each hidden layer,
activation functions for each hidden layers, and a generator object.
To use this class as a Keras model, the features and pre-processed adjacency matrix
should be supplied using either the :class:`FullBatchNodeGenerator` class for node inference
or the :class:`FullBatchLinkGenerator` class for link inference.
To have the appropriate pre-processing the generator object should be instanciated
with the `method='gcn'` argument.
Example:
Building an APPNP node model::
generator = FullBatchNodeGenerator(G, method="gcn")
ppnp = APPNP(
layer_sizes=[64, 64, 1],
activations=['relu', 'relu', 'relu'],
generator=generator,
dropout=0.5
)
x_in, x_out = ppnp.build()
Notes:
- The inputs are tensors with a batch dimension of 1. These are provided by the \
:class:`FullBatchNodeGenerator` object.
- This assumes that the normalized Laplacian matrix is provided as input to
Keras methods. When using the :class:`FullBatchNodeGenerator` specify the
``method='gcn'`` argument to do this pre-processing.
- The nodes provided to the :class:`FullBatchNodeGenerator.flow` method are
used by the final layer to select the predictions for those nodes in order.
However, the intermediate layers before the final layer order the nodes
in the same way as the adjacency matrix.
- The size of the final fully connected layer must be equal to the number of classes to predict.
Args:
layer_sizes (list of int): list of output sizes of fully connected layers in the stack
activations (list of str): list of activations applied to each fully connected layer's output
generator (FullBatchNodeGenerator): an instance of FullBatchNodeGenerator class constructed on the graph of interest
bias (bool): toggles an optional bias in fully connected layers
dropout (float): dropout rate applied to input features of each layer
kernel_regularizer (str): normalization applied to the kernels of fully connetcted layers
teleport_probability: "probability" of returning to the starting node in the propagation step as desribed in
the paper (alpha in the paper)
approx_iter: number of iterations to approximate PPNP as described in the paper (K in the paper)
"""
def __init__(
self,
layer_sizes,
generator,
activations,
bias=True,
dropout=0.0,
teleport_probability=0.1,
kernel_regularizer=None,
approx_iter=10,
):
if not isinstance(generator, FullBatchGenerator):
raise TypeError(
"Generator should be a instance of FullBatchNodeGenerator or FullBatchLinkGenerator"
)
if not len(layer_sizes) == len(activations):
raise ValueError(
"The number of layers should equal the number of activations"
)
if not isinstance(approx_iter, int) or approx_iter <= 0:
raise ValueError("approx_iter should be a positive integer")
if (teleport_probability > 1.0) or (teleport_probability < 0.0):
raise ValueError(
"teleport_probability should be between 0 and 1 (inclusive)"
)
self.layer_sizes = layer_sizes
self.teleport_probability = teleport_probability
self.activations = activations
self.bias = bias
self.dropout = dropout
self.kernel_regularizer = kernel_regularizer
self.support = 1
self.approx_iter = approx_iter
# Copy required information from generator
self.method = generator.method
self.multiplicity = generator.multiplicity
self.n_nodes = generator.features.shape[0]
self.n_features = generator.features.shape[1]
# Check if the generator is producing a sparse matrix
self.use_sparse = generator.use_sparse
if self.method == "none":
self.graph_norm_layer = GraphPreProcessingLayer(num_of_nodes=self.n_nodes)
self._layers = []
# Initialize a stack of fully connected layers
n_layers = len(self.layer_sizes)
for ii in range(n_layers):
l = self.layer_sizes[ii]
a = self.activations[ii]
self._layers.append(Dropout(self.dropout))
self._layers.append(
Dense(
l,
activation=a,
use_bias=self.bias,
kernel_regularizer=self.kernel_regularizer,
)
)
feature_dim = self.layer_sizes[-1]
for ii in range(approx_iter):
self._layers.append(Dropout(self.dropout))
self._layers.append(
APPNPPropagationLayer(
feature_dim,
teleport_probability=self.teleport_probability,
final_layer=(ii == (self.approx_iter - 1)),
)
)
def __call__(self, x):
"""
Apply APPNP to the inputs.
The input tensors are expected to be a list of the following:
[
Node features shape (1, N, F),
Adjacency indices (1, E, 2),
Adjacency values (1, E),
Output indices (1, O)
]
where N is the number of nodes, F the number of input features,
E is the number of edges, O the number of output nodes.
Args:
x (Tensor): input tensors
Returns:
Output tensor
"""
x_in, out_indices, *As = x
# Currently we require the batch dimension to be one for full-batch methods
batch_dim, n_nodes, _ = K.int_shape(x_in)
if batch_dim != 1:
raise ValueError(
"Currently full-batch methods only support a batch dimension of one"
)
# Convert input indices & values to a sparse matrix
if self.use_sparse:
A_indices, A_values = As
Ainput = [
SqueezedSparseConversion(
shape=(n_nodes, n_nodes), dtype=A_values.dtype
)([A_indices, A_values])
]
# Otherwise, create dense matrix from input tensor
else:
Ainput = [Lambda(lambda A: K.squeeze(A, 0))(A) for A in As]
# TODO: Support multiple matrices?
if len(Ainput) != 1:
raise NotImplementedError(
"The APPNP method currently only accepts a single matrix"
)
h_layer = x_in
for layer in self._layers[: (2 * len(self.layer_sizes))]:
h_layer = layer(h_layer)
feature_layer = h_layer
for layer in self._layers[(2 * len(self.layer_sizes)) :]:
if isinstance(layer, APPNPPropagationLayer):
h_layer = layer([h_layer, feature_layer, out_indices] + Ainput)
else:
# For other (non-graph) layers only supply the input tensor
h_layer = layer(h_layer)
return h_layer
[docs] def build(self, multiplicity=None):
"""
Builds an APPNP model for node or link prediction
Returns:
tuple: `(x_inp, x_out)`, where `x_inp` is a list of Keras/TensorFlow
input tensors for the model and `x_out` is a tensor of the model output.
"""
# Inputs for features
x_t = Input(batch_shape=(1, self.n_nodes, self.n_features))
# If not specified use multiplicity from instanciation
if multiplicity is None:
multiplicity = self.multiplicity
# Indices to gather for model output
if multiplicity == 1:
out_indices_t = Input(batch_shape=(1, None), dtype="int32")
else:
out_indices_t = Input(batch_shape=(1, None, multiplicity), dtype="int32")
# Create inputs for sparse or dense matrices
if self.use_sparse:
# Placeholders for the sparse adjacency matrix
A_indices_t = Input(batch_shape=(1, None, 2), dtype="int64")
A_values_t = Input(batch_shape=(1, None))
A_placeholders = [A_indices_t, A_values_t]
else:
# Placeholders for the dense adjacency matrix
A_m = Input(batch_shape=(1, self.n_nodes, self.n_nodes))
A_placeholders = [A_m]
# TODO: Support multiple matrices
x_inp = [x_t, out_indices_t] + A_placeholders
x_out = self(x_inp)
# Flatten output by removing singleton batch dimension
if x_out.shape[0] == 1:
self.x_out_flat = Lambda(lambda x: K.squeeze(x, 0))(x_out)
else:
self.x_out_flat = x_out
return x_inp, x_out
def link_model(self):
if self.multiplicity != 2:
warnings.warn(
"Link model requested but a generator not supporting links was supplied."
)
return self.build(multiplicity=2)
def node_model(self):
if self.multiplicity != 1:
warnings.warn(
"Node model requested but a generator not supporting nodes was supplied."
)
return self.build(multiplicity=1)
[docs] def propagate_model(self, base_model):
"""
Propagates a trained model using personalised PageRank.
Args:
base_model (keras Model): trained model with node features as input, predicted classes as output
returns:
tuple: `(x_inp, x_out)`, where `x_inp` is a list of two Keras input tensors
for the APPNP model (containing node features and graph adjacency),
and `x_out` is a Keras tensor for the APPNP model output.
"""
if self.multiplicity != 1:
raise RuntimeError(
"APPNP does not currently support propagating a link model"
)
out_indices_t = Input(batch_shape=(1, None), dtype="int32")
if self.use_sparse:
# Placeholders for the sparse adjacency matrix
A_indices_t = Input(batch_shape=(1, None, 2), dtype="int64")
A_values_t = Input(batch_shape=(1, None))
A_placeholders = [A_indices_t, A_values_t]
else:
# Placeholders for the dense adjacency matrix
A_m = Input(batch_shape=(1, self.n_nodes, self.n_nodes))
A_placeholders = [A_m]
if self.use_sparse:
A_indices, A_values = A_placeholders
Ainput = [
SqueezedSparseConversion(
shape=(self.n_nodes, self.n_nodes), dtype=A_values.dtype
)([A_indices, A_values])
]
# Otherwise, create dense matrix from input tensor
else:
Ainput = [Lambda(lambda A: K.squeeze(A, 0))(A) for A in A_placeholders]
# Inputs for features & target indices
x_t = Input(batch_shape=(1, self.n_nodes, self.n_features))
x_inp = [x_t, out_indices_t] + A_placeholders
# pass the node features through the base model
feature_layer = x_t
for layer in base_model.layers[1:]:
feature_layer = layer(feature_layer)
h_layer = feature_layer
# iterate through APPNPPropagation layers
for layer in self._layers[(2 * len(self.layer_sizes)) :]:
if isinstance(layer, APPNPPropagationLayer):
h_layer = layer([h_layer, feature_layer, out_indices_t] + Ainput)
else:
h_layer = layer(h_layer)
x_out = h_layer
return x_inp, x_out