论文标题
流形的卷积神经网络：从图和背面
Convolutional Neural Networks on Manifolds: From Graphs and Back
论文作者
论文摘要
近年来，由于从非欧几里得领域获得的更多可用数据，几何深度学习引起了很多关注。一些示例包括通信中3D模型的点云和无线传感器网络。图是连接这些离散数据点并捕获基础几何结构的常见模型。有了大量这些几何数据，任意尺寸的图形倾向于收敛到极限模型 - 歧管。深度神经网络体系结构已被证明是一种有力的技术，可以根据这些数据在歧管上解决问题。在本文中，我们提出了一个由多种卷积过滤器和点的非线性组成的歧管神经网络（MNN）。我们定义了一个多种卷积操作，该操作与离散图卷积一致，通过在空间和时域中离散。总而言之，我们将重点放在流形模型作为大图和构造MNN的极限上，而我们仍然可以通过MNN的离散化来带回图形神经网络。我们根据点云数据集进行实验，以展示我们提出的MNN的性能。
Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are common models to connect these discrete data points and capture the underlying geometric structure. With the large amount of these geometric data, graphs with arbitrarily large size tend to converge to a limit model -- the manifold. Deep neural network architectures have been proved as a powerful technique to solve problems based on these data residing on the manifold. In this paper, we propose a manifold neural network (MNN) composed of a bank of manifold convolutional filters and point-wise nonlinearities. We define a manifold convolution operation which is consistent with the discrete graph convolution by discretizing in both space and time domains. To sum up, we focus on the manifold model as the limit of large graphs and construct MNNs, while we can still bring back graph neural networks by the discretization of MNNs. We carry out experiments based on point-cloud dataset to showcase the performance of our proposed MNNs.
