In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

翻译：本文提出了一种新方法，用于检测带有属性顶点的无向图中的簇。我们通过创建额外的顶点和边（如[1,2]中所述）在增广图中融合顶点间的结构与属性相似性。随后将增广图嵌入到与其拉普拉斯矩阵相关的欧几里得空间中，并利用嵌入空间中的新型向量值距离，通过改进的K-means算法对顶点进行聚类。本方法属于早期融合方法（即在应用聚类之前将顶点附加信息与结构信息融合的方法），其主要创新在于将属性解释为图顶点的新实现，这些实现可作为相关欧几里得空间中的坐标向量进行处理。这使得我们能够扩展一种可扩展的广义谱聚类流程——通过线性时间复杂度的代数多重网格（AMG）方法，用被称为代数平滑向量的向量替代图拉普拉斯特征向量。我们通过与近期文献方法及公开结果的对比，讨论了所提聚类方法的性能。在多种合成数据集和真实属性图上的大量实验表明，当属性网络结构模糊时，我们的新算法（将属性信息嵌入聚类过程）优于仅基于结构的方法。此外，我们的新方法显著优于最初提出图增广的方法，证明了我们的嵌入策略和向量值距离在利用增广图表示方面具有显著优势。