Dynamic Graph Convolutional Networks Using the Tensor M-Product

Abstract

Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. In many of the real-world applications, the underlying graph changes over time, however, most of the existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs using a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor Mproduct technique. Theoretical results presented establish a connection between the proposed tensor approach and spectral convolution of tensors. The proposed method TM-GCN is consistent with the Message Passing Neural Network (MPNN) framework, accounting for both spatial and temporal message passing. Numerical experiments on realworld datasets demonstrate the performance of the proposed method for edge classification and link prediction tasks on dynamic graphs. We also consider an application related to the COVID-19 pandemic, and show how our method can be used for early detection of infected individuals from contact tracing data.

The Fréchet derivative of the tensor t-function

“…using the power series representation f (z) = ∞ α=0 a α z α . Inserting S ℓ1 E IJ (S T ) ℓ2 instead of C in relation (24), we find that…”

“…Remark 4. For "tubal vectors" A ∈ C 1×1×p , as they appear in certain tensor neural networks [24,27], the preceding discussion implies that all columns of K f (A) ∈ C p×p are shifted copies of the same vector. Thus, in this case, K f (A) is a circulant matrix.…”

“…This concept was generalized to functions of third-order tensors in [23], based on the tensor t-product formalism [5,19,20]; see also [25] for a further extension to so-called generalized tensor functions, which are functions of tensors with non-square faces. Functions (and generalized functions) of tensors have applications in deblurring of color images [28], tensor neural networks [24,27], multilinear dynamical systems [14], and the computation of the tensor nuclear norm [4].…”

Time-varying graph representation learning via higher-order skip-gram with negative sampling

“…Closely related to these ones are [ 50 ] and [ 51 ], which learn node vectors according to time-respecting random walks or spreading trajectory paths. Moreover, [ 52 ] proposed an embedding framework for user-item temporal interactions, and [ 53 ] suggested a tensor-based convolutional architecture for dynamic graphs.…”

Software Systems Implementation and Domain-Specific Architectures towards Graph Analytics

“…Therefore, studying efficient graph learning accelerators based on dynamic graph data is an important direction to explore. Compared with static graph learning, dynamic graph learning requires capturing the change of vertices over time, which is supported by introducing RNNs [191][192][193]. Notably, different types of dynamic graph learning may use different types of RNNs.…”