Graph Convolution with Low-rank Learnable Local Filters
Graph Convolution with Low-rank Learnable Local Filters
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发表时间：
2020-08
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通讯作者：
Xiuyuan Cheng;Zichen Miao;Qiang Qiu
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作者：
Xiuyuan Cheng;Zichen Miao;Qiang Qiu
旋转、缩放和视点变化等几何变化对视觉理解构成了重大挑战。一种常见的解决方案是直接模拟某些内在结构，例如使用地标。然而，建立有效的深度模型变得不容易，特别是当底层的非欧几里得网格不规则和粗糙时。最近使用图卷积的深度模型提供了一个适当的框架来处理这种非欧几里得数据，但其中许多模型，特别是那些基于全局图拉普拉斯的模型，缺乏表达能力，无法捕捉非欧几里得网格上信号表示所需的局部特征。本文提出了一种具有可学习的低秩局部滤波器的谱图卷积算法，该算法比以往的谱图卷积算法具有更好的表达能力。该模型还为谱图卷积和空间图卷积提供了统一的框架。为了提高模型的鲁棒性，引入了局部图拉普拉斯正则化。利用图滤波器的局部性和图的局部正则化，从理论上证明了对输入图数据扰动表示的稳定性。在球面网格数据、真实面部表情识别/基于骨骼的动作识别数据和模拟图噪声数据上的实验表明了该模型的经验优势。
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes non-trivial to build effective deep models, especially when the underlying non-Euclidean grid is irregular and coarse. Recent deep models using graph convolutions provide an appropriate framework to handle such non-Euclidean data, but many of them, particularly those based on global graph Laplacians, lack expressiveness to capture local features required for representation of signals lying on the non-Euclidean grid. The current paper introduces a new type of graph convolution with learnable low-rank local filters, which is provably more expressive than previous spectral graph convolution methods. The model also provides a unified framework for both spectral and spatial graph convolutions. To improve model robustness, regularization by local graph Laplacians is introduced. The representation stability against input graph data perturbation is theoretically proved, making use of the graph filter locality and the local graph regularization. Experiments on spherical mesh data, real-world facial expression recognition/skeleton-based action recognition data, and data with simulated graph noise show the empirical advantage of the proposed model.