Graph Neural Networks Explanation

How GNNs Work

Input: A graph structure with nodes and edges, where nodes represent entities, and edges represent relationships.
Neighbor Selection: - For each target node, its neighbors are identified based on graph connectivity. - Neighboring nodes provide local context for the target node.
Aggregation Function: - Combines the features of the selected neighbors. - Common aggregation methods include mean, sum, or max pooling.
Neural Network Transformation: - Aggregated features are passed through a neural network. - An activation function (e.g., ReLU, Sigmoid) introduces non-linearity to the transformations.
Updated Embedding: The target node’s representation is updated, reflecting its features and its neighborhood structure.
Applications: - Social networks (e.g., friend recommendations). - Knowledge graphs (e.g., inferring missing relationships). - Molecular property prediction. - Traffic prediction in road networks. - Fraud detection in financial networks.

Graph Neural Network (GNN) Code Example

Here's how we can define the layers of a simple Graph Neural Network (GNN):


import tensorflow as tf
from tensorflow.keras import layers
import tensorflow.keras.backend as K

class GraphConvolutionLayer(layers.Layer):
    def __init__(self, units, activation=None, **kwargs):
        super(GraphConvolutionLayer, self).__init__(**kwargs)
        self.units = units
        self.activation = activation

    def build(self, input_shape):
        self.kernel = self.add_weight(
            shape=(input_shape[1][-1], self.units),
            initializer="glorot_uniform",
            trainable=True
        )

    def call(self, inputs):
        adjacency_matrix, node_features = inputs
        # Graph convolution: A * X * W
        support = K.dot(node_features, self.kernel)
        output = K.dot(adjacency_matrix, support)
        if self.activation:
            output = self.activation(output)
        return output

# Define the GNN model
def build_gnn(num_nodes, num_node_features, num_classes):
    adjacency_matrix = layers.Input(shape=(num_nodes, num_nodes), name="adjacency_matrix")
    node_features = layers.Input(shape=(num_nodes, num_node_features), name="node_features")

    # Graph Convolution Layers
    x = GraphConvolutionLayer(32, activation=tf.nn.relu)([adjacency_matrix, node_features])
    x = GraphConvolutionLayer(16, activation=tf.nn.relu)([adjacency_matrix, x])

    # Global Average Pooling and Classification Layer
    x = layers.GlobalAveragePooling1D()(x)
    output = layers.Dense(num_classes, activation="softmax")(x)

    return tf.keras.Model(inputs=[adjacency_matrix, node_features], outputs=output)

# Instantiate the GNN model
gnn_model = build_gnn(num_nodes=10, num_node_features=5, num_classes=3)

Programming Ocean Academy

A Typical Graph Neural Network (GNN)

How GNNs Work

Graph Neural Network (GNN) Code Example