The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into spectral features in the Euclidean domain, and using them as the input points of classical kernels. However, this approach currently only takes into account features on vertices, whereas some graph datasets also support features on edges. In this work, we present a Gaussian process-based classification algorithm that can leverage one or both vertex and edges features. Furthermore, we take advantage of the Hodge decomposition to better capture the intricate richness of vertex and edge features, which can be beneficial on diverse tasks.

翻译：图分类问题在机器学习中普遍存在。尽管通常采用图神经网络或图核方法，但高斯过程可通过将图域的空间特征转换为欧几里得域中的谱特征，并将其用作经典核函数的输入点来实现。然而，当前该方法仅考虑顶点上的特征，而某些图数据集还支持边上的特征。在本研究中，我们提出了一种基于高斯过程的分类算法，能够利用顶点特征、边特征或两者。此外，我们利用Hodge分解来更好地捕捉顶点和边特征的复杂丰富性，这在多样化任务中可能具有优势。