Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
复制标题
DOI：
--
复制
发表时间：
2019-05
期刊：
影响因子：
--
通讯作者：
Michael Perlmutter;Feng Gao;Guy Wolf;M. Hirn
中科院分区：
文献类型：
--
作者：
Michael Perlmutter;Feng Gao;Guy Wolf;M. Hirn
欧几里德散射变换是在近十年前引入的，旨在提高对卷积神经网络的数学理解。受最近对几何深度学习的兴趣的启发，其目的是将卷积神经网络推广到流形和图形结构域，我们定义了流形上的几何散射变换。类似于欧几里德散射变换，几何散射变换是基于小波滤波器和逐点非线性的级联。它对局部等距是不变的，对某些类型的超同态是稳定的。实验结果表明，它的实用性在几个几何学习任务。我们的结果概括了变形稳定性和局部平移不变性的欧几里得散射，并证明了连接所使用的过滤器结构的数据的底层几何的重要性。
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.