论文标题
在图形上重新审视卷积神经网络，该图具有Laplace-Beltrami光谱滤波的多项式近似值
Revisiting convolutional neural network on graphs with polynomial approximations of Laplace-Beltrami spectral filtering
论文作者
论文摘要
本文重新审视了Defferrard（2016）中给出的光谱图卷积神经网络（图形CNN），并通过用LB操作员替换图形Laplacian来开发Laplace-Beltrami CNN（LB-CNN）。然后，我们通过图表上的LB操作员定义光谱过滤器。我们探讨了Chebyshev，Laguerre和Hermite多项式的可行性，以近似基于LB的光谱过滤器，并定义了LB操作员以在LBCNN中汇总的更新。我们采用了来自阿尔茨海默氏病神经影像倡议（ADNI）的大脑图像数据，并证明了拟议的LB-CNN的使用。基于ADNI数据集的皮质厚度，我们表明LB-CNN与光谱图CNN相比没有提高分类精度。这三个多项式具有相似的计算成本，并且在LB-CNN或光谱图中显示出可比的分类精度。我们的发现表明，即使三个多项式的形状不同，深度学习架构也使我们能够学习光谱过滤器，从而使分类性能不依赖于多项式或操作员的类型（图Laplacian和LB运算符）。
This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace-Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator. We then define spectral filters via the LB operator on a graph. We explore the feasibility of Chebyshev, Laguerre, and Hermite polynomials to approximate LB-based spectral filters and define an update of the LB operator for pooling in the LBCNN. We employ the brain image data from Alzheimer's Disease Neuroimaging Initiative (ADNI) and demonstrate the use of the proposed LB-CNN. Based on the cortical thickness of the ADNI dataset, we showed that the LB-CNN didn't improve classification accuracy compared to the spectral graph-CNN. The three polynomials had a similar computational cost and showed comparable classification accuracy in the LB-CNN or spectral graph-CNN. Our findings suggest that even though the shapes of the three polynomials are different, deep learning architecture allows us to learn spectral filters such that the classification performance is not dependent on the type of the polynomials or the operators (graph Laplacian and LB operator).
