Graph Neural Networks have recently become a prevailing paradigm for various high-impact graph analytical problems. Existing efforts can be mainly categorized as spectral-based and spatial-based methods. The major challenge for the former is to find an appropriate graph filter to distill discriminative information from input signals for learning. Recently, myriads of explorations are made to achieve better graph filters, e.g., Graph Convolutional Network (GCN), which leverages Chebyshev polynomial truncation to seek an approximation of graph filters and bridge these two families of methods. Nevertheless, it has been shown in recent studies that GCN and its variants are essentially employing fixed low-pass filters to perform information denoising. Thus their learning capability is rather limited and may over-smooth node representations at deeper layers. To tackle these problems, we develop a novel graph neural network framework AdaGNN with a well-designed adaptive frequency response filter. At its core, AdaGNN leverages a simple but elegant trainable filter that spans across multiple layers to capture the varying importance of different frequency components for node representation learning. The inherent differences among different feature channels are also well captured by the filter. As such, it empowers AdaGNN with stronger expressiveness and naturally alleviates the over-smoothing problem. We empirically validate the effectiveness of the proposed framework on various benchmark datasets. Theoretical analysis is also provided to show the superiority of the proposed AdaGNN. The open-source implementation of AdaGNN can be found here: https://github.com/yushundong/AdaGNN.
Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach
National University of Singapore（新加坡国立大学）；OPPO Shenzhen Research Institute（OPPO深圳研究院）；Micro Connect Technology, China（中国微联通技术公司）；University of Cambridge（剑桥大学）
Robust Adaptive Filtering Based on Exponential Functional Link Network
Southwest Petroleum University（西南石油大学）；Southwest University of Science and Technology（西南科技大学）；Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）；University of York（约克大学）
Study of Sparsity-Aware Subband Adaptive Filtering Algorithms with Adjustable Penalties
Southwest University of Science and Technology（西南科技大学）；Southwest Jiaotong University（西南交通大学）；PUC-Rio（里约热内卢天主教大学）；University of York（约克大学）；Sichuan University（四川大学）
