Читать книгу Artificial Intelligence and Quantum Computing for Advanced Wireless Networks - Savo G. Glisic - Страница 76

Directed graphs: Directed edges can yield more information than undirected edges. For example, in a knowledge graph where the edge starts from the head entity and ends at the tail entity, the head entity is the parent class of the tail entity, which suggests we should treat the information propagation process from parent classes and child classes differently. Here, we use two kinds of weight matrix, W_p and W_c , to incorporate more precise structural information. The propagation rule is [3]

(5.5)

where are the normalized adjacency matrix for parents and children, respectively, and σ denotes a nonlinear activation function.

Heterogeneous graphs: These have several kinds of nodes. The simplest way to process heterogeneous graphs is to convert the type of each node to a one‐hot feature vector that is concatenated with the original feature. GraphInception [4] introduces the concept of metapath into propagation on the heterogeneous graph. With metapath, we can group neighbors according to their node types and distances. For each neighbor group, GraphInception treats it as a subgraph in a homogeneous graph to perform propagation and concatenates the propagation results from different homogeneous graphs to arrive at a collective node representation. In [5], the heterogeneous graph attention network (HAN) was proposed, which utilizes node‐level and semantic‐level attention. The model has the ability to consider node importance and meta‐paths simultaneously.

Graphs with edge information: Here, each edge has additional information like the weight or the type of the edge. There are two ways to handle this kind of graph:

1 We can convert the graph to a bipartite graph where the original edges also become nodes and one original edge is split into two new edges, which means there are two new edges between the edge node and begin/end nodes. The encoder of GS2 (Graph to Sequence) [6] uses the following aggregation function for neighbors:(5.6) where Wr and br are the propagation parameters for different types of edges (relations r), ρ is a nonlinearity, ⊙ stands for the Hadamard product and is the set of neighboring nodes.

2 We can adapt different weight matrices for propagation on different kinds of edges. When the number of relations is very large, r‐GCN (Relational Data with Graph Convolutional Networks) [7] introduces two kinds of regularization to reduce the number of parameters for modeling relations: basis‐ and block‐diagonal‐decomposition. With the basis decomposition, each Wr is defined as follows:(5.7)

Here each W_r is a linear combination of basis transformations with coefficients a_rb . In the blockdiagonal decomposition, r‐GCN defines each W_r through the direct sum over a set of low‐dimensional matrices, which needs more parameters than the first one.

Dynamic graphs: These have a static graph structure and dynamic input signals. To capture both kinds of information, diffusion convolutional recurrent NN (DCRNN) [8] and spatial‐temporal graph convolutional networks (STGCN) [9] first collect spatial information by GNNs, then feed the outputs into a sequence model like sequence‐to‐sequence model or convolutional neural networks (CNNs). On the other hand, structural‐recurrent NN [10] and STGCN [11] collect spatial and temporal messages at the same time. They extend the static graph structure with temporal connections so that they can apply traditional GNNs to the extended graphs.