论文标题
谎言组代数的代数卷积过滤器
Algebraic Convolutional Filters on Lie Group Algebras
论文作者
论文摘要
组卷积神经网络是使用已知在信号中的对称性的有用工具。但是，他们要求信号在组本身上定义。现有的方法要么直接与组信号一起使用，要么施加了启发式的提升步骤来计算卷积，这可能是计算昂贵的。从代数信号处理的角度来看，我们直接提出了一个新型的卷积过滤器，从而直接从谎言组代数中提出，从而消除了完全提升的需求。此外，我们通过与多编码信号处理的连接来建立过滤器的稳定性。在两个数据集上的分类问题上评估了所提出的过滤器，该数据集的$（3）$组对称。
Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or they impose a lifting step with heuristics to compute the convolution which can be computationally costly. Taking an algebraic signal processing perspective, we propose a novel convolutional filter from the Lie group algebra directly, thereby removing the need to lift altogether. Furthermore, we establish stability of the filter by drawing connections to multigraph signal processing. The proposed filter is evaluated on a classification problem on two datasets with $SO(3)$ group symmetries.
