基于低秩可学习局部滤波器的图卷积
Graph Convolution with Low-rank Learnable Local Filters
摘要：
几何变化，如旋转，缩放和视点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对某些内在结构进行建模，例如，使用地标。然而，构建有效的深度模型变得非常重要，特别是当底层非欧几里得网格不规则且粗糙时。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德数据，但其中许多模型，特别是基于全局图拉普拉斯算子的模型，缺乏表达能力来捕获表示非欧几里德网格上的信号所需的局部特征。本文介绍了一种新型的图卷积与可学习的低秩局部滤波器，这是证明比以前的谱图卷积方法更有表现力。该模型还为谱卷积和空间图卷积提供了一个统一的框架。为了提高模型的鲁棒性，引入了局部图拉普拉斯正则化。利用图滤波局部性和局部图正则化理论证明了该表示对输入图数据扰动的稳定性。球形网格数据，真实世界的面部表情识别/基于动作识别数据，和模拟图形噪声的数据上的实验表明，所提出的模型的经验优势。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
