Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and undirected graphs that form a global multilayer graph, where the common vertex set represents the entities and the edges on different layers capture the similarities of the entities in term of the different modalities. In this paper, we address the problem of analyzing multi-layer graphs and propose methods for clustering the vertices by efficiently merging the information provided by the multiple modalities. To this end, we propose to combine the characteristics of individual graph layers using tools from subspace analysis on a Grassmann manifold. The resulting combination can then be viewed as a low dimensional representation of the original data which preserves the most important information from diverse relationships between entities. We use this information in new clustering methods and test our algorithm on several synthetic and real world datasets where we demonstrate superior or competitive performances compared to baseline and state-of-the-art techniques. Our generic framework further extends to numerous analysis and learning problems that involve different types of information on graphs.

本文提出了一种分析多层图并通过在Grassmann流形上使用子空间分析工具来结合个体图层特征的方法。 这种方法可以视为原始数据的低维表示，其中保留了实体之间不同关系的最重要信息，并可用于聚类。 在多个数据集上的实验结果表明，该算法具有优异的性能和竞争力。

利用 Grassmann 流形上的子空间分析在多层图上进行聚类