Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis.

Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs.

Graph neural networks (GNNs) learn the representation of nodes in a graph by aggregating the neighborhood information in various ways. As these networks grow in depth, their receptive field grows exponentially due to the increase in neighborhood sizes, resulting in high memory costs. Graph sampling solves memory issues in GNNs by sampling a small ratio of the nodes in the graph. This way, GNNs can scale to much larger graphs. Most sampling methods focus on fixed sampling heuristics, which may not generalize to different structures or tasks. We introduce GRAPES, an adaptive graph sampling method that learns to identify sets of influential nodes for training a GNN classifier. GRAPES uses a GFlowNet to learn node sampling probabilities given the classification objectives. We evaluate GRAPES across several small- and large-scale graph benchmarks and demonstrate its effectiveness in accuracy and scalability. In contrast to existing sampling methods, GRAPES maintains high accuracy even with small sample sizes and, therefore, can scale to very large graphs. Our code is publicly available at https://github.com/dfdazac/grapes.

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on continuous Gaussian perturbations. Instead, in this work, we suggest using discrete noise for the forward Markov process. This ensures that in every intermediate step the graph remains discrete. Compared to the previous approach, our experimental results on four datasets and multiple architectures show that using a discrete noising process results in higher quality generated samples indicated with an average MMDs reduced by a factor of 1.5. Furthermore, the number of denoising steps is reduced from 1000 to 32 steps, leading to a 30 times faster sampling procedure.

Transferring knowledge across graphs plays a pivotal role in many high-stake domains, ranging from transportation networks to e-commerce networks, from neuroscience to finance. To date, the vast majority of existing works assume both source and target domains are sampled from a universal and stationary distribution. However, many real-world systems are intrinsically dynamic, where the underlying domains are evolving over time. To bridge the gap, we propose to shift the problem to the dynamic setting and ask: given the label-rich source graphs and the label-scarce target graphs observed in previous T timestamps, how can we effectively characterize the evolving domain discrepancy and optimize the generalization performance of the target domain at the incoming T+1 timestamp? To answer the question, for the first time, we propose a generalization bound under the setting of dynamic transfer learning across graphs, which implies the generalization performance is dominated by domain evolution and domain discrepancy between source and target domains. Inspired by the theoretical results, we propose a novel generic framework DyTrans to improve knowledge transferability across dynamic graphs. In particular, we start with a transformer-based temporal encoding module to model temporal information of the evolving domains; then, we further design a dynamic domain unification module to efficiently learn domain-invariant representations across the source and target domains. Finally, extensive experiments on various real-world datasets demonstrate the effectiveness of DyTrans in transferring knowledge from dynamic source domains to dynamic target domains.

Node embedding is a central topic in graph representation learning. Computational efficiency and scalability can be challenging to any method that requires full-graph operations. We propose sampling approaches to node embedding, with or without explicit modelling of the feature vector, which aim to extract useful information from both the eigenvectors related to the graph Laplacien and the given values associated with the graph.

Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally, applying the same definition to the whole graph or any given subgraph of it would result in systematically different network functions. In this paper we consider the feasibility of graph sampling approach to network function learning, as well as the corresponding learning methods based on the sample graphs. This can be useful either when the edges are unknown to start with or the graph is too large (or dynamic) to be processed entirely. Potentially more realistic contextual features can be engineered in terms of the neighbour function (2), which must be invariant over permutations of the adjacent nodes.

This project describes the application of the technologies of Machine Learning and Internet-of-Things to assess the lower limb strength of individuals undergoing rehabilitation or therapy. Specifically, it seeks to measure and assess the progress of individuals by sensors attached to chairs and processing the data through Google GPU Tensorflow CoLab. Pressure sensors are attached to various locations on a chair, including but not limited to the seating area, backrest, hand rests, and legs. Sensor data from the individual performing both sit-to-stand transition and stand-to-sit transition provides a time series dataset regarding the pressure distribution and vibratory motion on the chair. The dataset and timing information can then be fed into a machine learning model to estimate the relative strength and weakness during various phases of the movement.

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of the embeddings of their sample graphs. In particular, the graph models that we consider arise from graphons, which are the most general possible parameterizations of infinite exchangeable graph models and which are the central objects of study in the theory of dense graph limits. We exhibit an infinite class of graphons that are well-separated in terms of cut distance and are indistinguishable by a GCN with nonlinear activation functions coming from a certain broad class if its depth is at least logarithmic in the size of the sample graph. These results theoretically match empirical observations of several prior works. Finally, we show a converse result that for pairs of graphons satisfying a degree profile separation property, a very simple GCN architecture suffices for distinguishability. To prove our results, we exploit a connection to random walks on graphs.

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of the embeddings of their sample graphs. In particular, the graph models that we consider arise from graphons, which are the most general possible parameterizations of infinite exchangeable graph models and which are the central objects of study in the theory of dense graph limits. We exhibit an infinite class of graphons that are well-separated in terms of cut distance and are indistinguishable by a GCN with nonlinear activation functions coming from a certain broad class if its depth is at least logarithmic in the size of the sample graph, and furthermore show that, for this application, ReLU activation functions and non-identity weight matrices with non-negative entries do not help in terms of distinguishing power. These results theoretically match empirical observations of several prior works. Finally, we show that for pairs of graphons satisfying a degree profile separation property, a very simple GCN architecture suffices for distinguishability. To prove our results, we exploit a connection to random walks on graphs.