Finding the mean of sampled data is a fundamental task in machine learning
and statistics. However, in cases where the data samples are graph objects,
defining a mean is an inherently difficult task. We propose a novel framework
for defining a graph mean via embeddings in the space of smooth graph signal
distributions, where graph similarity can be measured using the Wasserstein
metric. By finding a mean in this embedding space, we can recover a mean graph
that preserves structural information. We establish the existence and
uniqueness of the novel graph mean, and provide an iterative algorithm for
computing it. To highlight the potential of our framework as a valuable tool
for practical applications in machine learning, it is evaluated on various
tasks, including k-means clustering of structured graphs, classification of
functional brain networks, and semi-supervised node classification in
multi-layer graphs. Our experimental results demonstrate that our approach
achieves consistent performance, outperforms existing baseline approaches, and
improves state-of-the-art methods.

本文提出了一种基于嵌入空间和 Wasserstein 距离度量的图平均值定义框架，可通过迭代算法计算得出可保留结构信息的均值图，该框架在结构图聚类、功能脑网络分类和半监督节点分类中表现优异，是一个有价值的实用工具。