With the rise and advent of graph learning techniques, graph data has become ubiquitous. However, while several efforts are being devoted to the design of new convolutional architectures, pooling or positional encoding schemes, less effort is being spent on problems involving maps between (possibly very large) graphs, such as signal transfer, graph isomorphism and subgraph correspondence. With this paper, we anticipate the need for a convenient framework to deal with such problems, and focus in particular on the challenging subgraph alignment scenario. We claim that, first and foremost, the representation of a map plays a central role on how these problems should be modeled. Taking the hint from recent work in geometry processing, we propose the adoption of a spectral representation for maps that is compact, easy to compute, robust to topological changes, easy to plug into existing pipelines, and is especially effective for subgraph alignment problems. We report for the first time a surprising phenomenon where the partiality arising in the subgraph alignment task is manifested as a special structure of the map coefficients, even in the absence of exact subgraph isomorphism, and which is consistently observed over different families of graphs up to several thousand nodes.
翻译:随着图表学习技术的上升和出现,图表数据已变得无处不在。然而,虽然在设计新的革命结构、集合或定位编码计划方面正在作出一些努力,但对于(可能非常大)图形之间的地图问题,例如信号传输、图形异形学和子图对应等,我们花的精力却较少。有了本文件,我们预计需要有一个方便的框架来处理这些问题,并特别侧重于具有挑战性的子图协调设想。我们声称,首先,地图的表示方式在如何建模这些问题上起着中心作用。根据最近几何学处理工作中的提示,我们提议为紧凑、易于编译、易于进行地形变化的光谱代表方式,容易插入现有的管道,而且对于子图协调问题特别有效。我们首次报告一个令人惊讶的现象,即子图协调任务中出现的偏差表现为地图系数的特殊结构,即使没有精确的子谱系系,也始终在不同的图表中观察到。