论文标题
在半换档不变图过滤器上
On semi shift invariant graph filters
论文作者
论文摘要
在图形信号处理中，最重要的主题之一是对滤镜的过滤器的研究，即捕获图信号之间关系的线性变换。过滤器最重要的家族之一是换档不变过滤器的空间，定义为使用首选的图形移动运算符的转换通勤。换档不变过滤器在图形信号处理和图形神经网络中具有广泛的应用。可以将移位不变过滤器用几何解释为信息聚合过程（来自本地邻域），并且可以使用矩阵乘法轻松计算。但是，在应用程序中使用仅移动不变过滤器（例如具有限制性均匀的均匀过滤器）仍然存在缺点。在本文中，我们通过引入和研究半换档不变过滤器来概括不变过滤器。我们通过新的信号处理框架（子图信号处理）提供了半换档不变过滤器的应用。此外，我们还展示了如何在图形神经网络中使用半偏移不变过滤器。
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant filters, defined as transformations commute with a preferred graph shift operator. Shift invariant filters have a wide range of applications in graph signal processing and graph neural networks. A shift invariant filter can be interpreted geometrically as an information aggregation procedure (from local neighborhood), and can be computed easily using matrix multiplication. However, there are still drawbacks to using solely shift invariant filters in applications, such as being restrictively homogeneous. In this paper, we generalize shift invariant filters by introducing and studying semi shift invariant filters. We give an application of semi shift invariant filters with a new signal processing framework, the subgraph signal processing. Moreover, we also demonstrate how semi shift invariant filters can be used in graph neural networks.
