Yu Jin

Yu Jin, Andreas Loukas, Joseph F. JaJa

Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph coarsening techniques are commonly used to reduce the computational load while attempting to maintain the basic structural properties of the original graph. As there is no consensus on the specific graph properties preserved by coarse graphs, how to measure the differences between original and coarse graphs remains a key challenge. In this work, we introduce a new perspective regarding the graph coarsening based on concepts from spectral graph theory. We propose and justify new distance functions that characterize the differences between original and coarse graphs. We show that the proposed spectral distance naturally captures the structural differences in the graph coarsening process. In addition, we provide efficient graph coarsening algorithms to generate graphs which provably preserve the spectral properties from original graphs. Experiments show that our proposed algorithms consistently achieve better results compared to previous graph coarsening methods on graph classification and block recovery tasks.

Shengyu Zhang, Kun Kuang, Jiezhong Qiu et al.

Graph is a flexible and effective tool to represent complex structures in practice and graph neural networks (GNNs) have been shown to be effective on various graph tasks with randomly separated training and testing data. In real applications, however, the distribution of training graph might be different from that of the test one (e.g., users' interactions on the user-item training graph and their actual preference on items, i.e., testing environment, are known to have inconsistencies in recommender systems). Moreover, the distribution of test data is always agnostic when GNNs are trained. Hence, we are facing the agnostic distribution shift between training and testing on graph learning, which would lead to unstable inference of traditional GNNs across different test environments. To address this problem, we propose a novel stable prediction framework for GNNs, which permits both locally and globally stable learning and prediction on graphs. In particular, since each node is partially represented by its neighbors in GNNs, we propose to capture the stable properties for each node (locally stable) by re-weighting the information propagation/aggregation processes. For global stability, we propose a stable regularizer that reduces the training losses on heterogeneous environments and thus warping the GNNs to generalize well. We conduct extensive experiments on several graph benchmarks and a noisy industrial recommendation dataset that is collected from 5 consecutive days during a product promotion festival. The results demonstrate that our method outperforms various SOTA GNNs for stable prediction on graphs with agnostic distribution shift, including shift caused by node labels and attributes.

Yu Jin, Joseph F. JaJa

Recently a variety of methods have been developed to encode graphs into low-dimensional vectors that can be easily exploited by machine learning algorithms. The majority of these methods start by embedding the graph nodes into a low-dimensional vector space, followed by using some scheme to aggregate the node embeddings. In this work, we develop a new approach to learn graph-level representations, which includes a combination of unsupervised and supervised learning components. We start by learning a set of node representations in an unsupervised fashion. Graph nodes are mapped into node sequences sampled from random walk approaches approximated by the Gumbel-Softmax distribution. Recurrent neural network (RNN) units are modified to accommodate both the node representations as well as their neighborhood information. Experiments on standard graph classification benchmarks demonstrate that our proposed approach achieves superior or comparable performance relative to the state-of-the-art algorithms in terms of convergence speed and classification accuracy. We further illustrate the effectiveness of the different components used by our approach.