Читать книгу Artificial Intelligence and Quantum Computing for Advanced Wireless Networks - Savo G. Glisic - Страница 83

These networks are designed to capture the dynamics of graphs. STGNNs follow two directions, recurrent neural network (RNN)‐based methods and CNN‐based methods. Most RNN‐based approaches capture spatial‐temporal dependencies by filtering inputs and hidden states passed to a recurrent unit using graph convolutions. To illustrate this (see Figure 5.7), suppose a simple RNN takes the form

(5.70)

where X^(t) ∈ R^{n × d} is the node feature matrix at time step t. After inserting graph convolution, Eq. (5.70) becomes

(5.71)

where Gconv (·) is a graph convolutional layer. The Graph Convolutional Recurrent Network (GCRN) combines a LSTM network with ChebNet. DCRNN incorporates a proposed DGC layer (Eq. (5.50)) into a GRU network.

Previous methods all use a predefined graph structure. They assume the predefined graph structure reflects the genuine dependency relationships among nodes. However, with many snapshots of graph data in a spatial‐temporal setting, it is possible to learn latent static graph structures automatically from data. To realize this,

Figure 5.7 A STGNN for spatial‐temporal graph forecasting. A graph convolutional layer is followed by a 1D‐CNN layer. The graph convolutional layer operates on A and X(t) to capture the spatial dependency, while the 1D‐CNN layer slides over X along the time axis to capture the temporal dependency. The output layer is a linear transformation, generating a prediction for each node, such as its future value at the next time step.

Source: Wu et al. [38].

Graph WaveNet [61] proposes a self‐adaptive adjacency matrix to perform graph convolutions. The self‐adaptive adjacency matrix is defined as

(5.72)

where the softmax function is computed along the row dimension, E1 denotes the source node embedding, and E2 denotes the target node embedding with learnable parameters. By multiplying E1 with E2, one can get the dependency weight between a source node and a target node. With a complex CNN‐based spatial‐temporal neural network, Graph WaveNet performs well without being given an adjacency matrix.