Xuebin Zheng

Bingxin Zhou, Xuebin Zheng, Yu Guang Wang et al.

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's similarity relationship in the embedded space needs specific tools and a similarity metric. This paper develops a new graph representation learning scheme, namely EGG, which embeds approximated second-order graph characteristics into a Grassmann manifold. The proposed strategy leverages graph convolutions to learn hidden representations of the corresponding subspace of the graph, which is then mapped to a Grassmann point of a low dimensional manifold through truncated singular value decomposition (SVD). The established graph embedding approximates denoised correlationship of node attributes, as implemented in the form of a symmetric matrix space for Euclidean calculation. The effectiveness of EGG is demonstrated using both clustering and classification tasks at the node level and graph level. It outperforms baseline models on various benchmarks.

Mengxi Yang, Dai Shi, Xuebin Zheng et al.

This paper aims to provide a novel design of a multiscale framelet convolution for spectral graph neural networks (GNNs). While current spectral methods excel in various graph learning tasks, they often lack the flexibility to adapt to noisy, incomplete, or perturbed graph signals, making them fragile in such conditions. Our newly proposed framelet convolution addresses these limitations by decomposing graph data into low-pass and high-pass spectra through a finely-tuned multiscale approach. Our approach directly designs filtering functions within the spectral domain, allowing for precise control over the spectral components. The proposed design excels in filtering out unwanted spectral information and significantly reduces the adverse effects of noisy graph signals. Our approach not only enhances the robustness of GNNs but also preserves crucial graph features and structures. Through extensive experiments on diverse, real-world graph datasets, we demonstrate that our framelet convolution achieves superior performance in node classification tasks. It exhibits remarkable resilience to noisy data and adversarial attacks, highlighting its potential as a robust solution for real-world graph applications. This advancement opens new avenues for more adaptive and reliable spectral GNN architectures.

Bingxin Zhou, Ruikun Li, Xuebin Zheng et al.

As graph data collected from the real world is merely noise-free, a practical representation of graphs should be robust to noise. Existing research usually focuses on feature smoothing but leaves the geometric structure untouched. Furthermore, most work takes L2-norm that pursues a global smoothness, which limits the expressivity of graph neural networks. This paper tailors regularizers for graph data in terms of both feature and structure noises, where the objective function is efficiently solved with the alternating direction method of multipliers (ADMM). The proposed scheme allows to take multiple layers without the concern of over-smoothing, and it guarantees convergence to the optimal solutions. Empirical study proves that our model achieves significantly better performance compared with popular graph convolutions even when the graph is heavily contaminated.

Xuebin Zheng, Bingxin Zhou, Junbin Gao et al.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass frequencies coefficients for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds high-frequency information at different scales. Compared to ReLU, shrinkage activation improves model performance on denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with well-preserved prediction performance.

Xuebin Zheng, Bingxin Zhou, Yu Guang Wang et al.

Graph representation learning has many real-world applications, from super-resolution imaging, 3D computer vision to drug repurposing, protein classification, social networks analysis. An adequate representation of graph data is vital to the learning performance of a statistical or machine learning model for graph-structured data. In this paper, we propose a novel multiscale representation system for graph data, called decimated framelets, which form a localized tight frame on the graph. The decimated framelet system allows storage of the graph data representation on a coarse-grained chain and processes the graph data at multi scales where at each scale, the data is stored at a subgraph. Based on this, we then establish decimated G-framelet transforms for the decomposition and reconstruction of the graph data at multi resolutions via a constructive data-driven filter bank. The graph framelets are built on a chain-based orthonormal basis that supports fast graph Fourier transforms. From this, we give a fast algorithm for the decimated G-framelet transforms, or FGT, that has linear computational complexity O(N) for a graph of size N. The theory of decimated framelets and FGT is verified with numerical examples for random graphs. The effectiveness is demonstrated by real-world applications, including multiresolution analysis for traffic network, and graph neural networks for graph classification tasks.

Xuebin Zheng, Bingxin Zhou, Ming Li et al.

Graph Neural Networks (GNNs) have recently caught great attention and achieved significant progress in graph-level applications. In this paper, we propose a framework for graph neural networks with multiresolution Haar-like wavelets, or MathNet, with interrelated convolution and pooling strategies. The underlying method takes graphs in different structures as input and assembles consistent graph representations for readout layers, which then accomplishes label prediction. To achieve this, the multiresolution graph representations are first constructed and fed into graph convolutional layers for processing. The hierarchical graph pooling layers are then involved to downsample graph resolution while simultaneously remove redundancy within graph signals. The whole workflow could be formed with a multi-level graph analysis, which not only helps embed the intrinsic topological information of each graph into the GNN, but also supports fast computation of forward and adjoint graph transforms. We show by extensive experiments that the proposed framework obtains notable accuracy gains on graph classification and regression tasks with performance stability. The proposed MathNet outperforms various existing GNN models, especially on big data sets.

Bingxin Zhou, Xuebin Zheng, Junbin Gao

Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on large-scale sparse datasets with high computational efficiency. In this paper, we present a new framework for Adam-type methods with the trend information when updating the parameters with the adaptive step size and gradients. The additional terms in the algorithm promise an efficient movement on the complex cost surface, and thus the loss would converge more rapidly. We show empirically the importance of adding the trend component, where our framework outperforms the conventional Adam and AMSGrad methods constantly on the classical models with several real-world datasets.