Over the last few years, we have witnessed the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high interest because of their potential in processing graph-structured data. In particular, there is a strong interest in exploring the possibilities in performing convolution on graphs using an extension of the GNN architecture, generally referred to as Graph Convolutional Neural Networks (ConvGNN). Convolution on graphs has been achieved mainly in two forms: spectral and spatial convolutions. Due to the higher flexibility in exploring and exploiting the graph structure of data, there is recently an increasing interest in investigating the possibilities that the spatial approach can offer. The idea of finding a way to adapt the network behaviour to the inputs they process to maximize the total performances has aroused much interest in the neural networks literature over the years. This paper presents a novel method to adapt the behaviour of a ConvGNN to the input proposing a method to perform spatial convolution on graphs using input-specific filters, which are dynamically generated from nodes feature vectors. The experimental assessment confirms the capabilities of the proposed approach, which achieves satisfying results using a low number of filters.

翻译：近年来，我们见证了由非欧几里得域生成的日益增长的数据，这些数据通常表示为具有复杂关系的图结构，而图神经网络因其在处理图结构数据方面的潜力而受到高度关注。特别是，利用图神经网络架构的扩展（通常称为图卷积神经网络）在图上执行卷积操作的可能性引发了强烈兴趣。图上的卷积主要通过两种形式实现：谱域卷积和空间域卷积。由于空间方法在探索和利用数据的图结构方面具有更高的灵活性，近年来对其所能提供的可能性进行的研究日益增多。寻找一种使网络行为适应其处理输入以最大化总体性能的方法，在神经网络文献中多年来一直备受关注。本文提出了一种使图卷积神经网络行为适应输入的新方法，该方法通过从节点特征向量动态生成输入特定滤波器来执行图上的空间卷积。实验评估证实了该方法的有效性，并在使用少量滤波器的情况下取得了令人满意的结果。