Graph feature extraction is a fundamental task in graphs analytics. Using feature vectors (graph descriptors) in tandem with data mining algorithms that operate on Euclidean data, one can solve problems such as classification, clustering, and anomaly detection on graph-structured data. This idea has proved fruitful in the past, with spectral-based graph descriptors providing state-of-the-art classification accuracy on benchmark datasets. However, these algorithms do not scale to large graphs since: 1) they require storing the entire graph in memory, and 2) the end-user has no control over the algorithm's runtime. In this paper, we present single-pass streaming algorithms to approximate structural features of graphs (counts of subgraphs of order $k \geq 4$). Operating on edge streams allows us to avoid keeping the entire graph in memory, and controlling the sample size enables us to control the time taken by the algorithm. We demonstrate the efficacy of our descriptors by analyzing the approximation error, classification accuracy, and scalability to massive graphs. Our experiments showcase the effect of the sample size on approximation error and predictive accuracy. The proposed descriptors are applicable on graphs with millions of edges within minutes and outperform the state-of-the-art descriptors in classification accuracy.

翻译：图形分析分析中, 地貌图特征提取是一项基本任务。 使用地貌矢量( 绘图描述器) 来配合在 Euclidean 数据上运行的数据挖掘算法, 人们可以解决图表结构化数据分类、 集群和异常探测等问题。 这个想法在过去已经证明富有成效, 光谱图形描述器在基准数据集上提供最新水平的分类精确度。 然而, 这些算法在以下情况下不会向大图表缩放:1) 它们需要将整张图存储在记忆中, 2) 终端用户无法控制算法的运行时间。 在本文中, 我们提出单子流算法, 以近似图形的结构特征( $k\geq 4$的子图数) 。 在边缘流操作中, 使我们能够避免将整张图保存在记忆中, 并控制样本大小, 使我们能够控制算法的时间。 我们通过分析近似误、 分类精确度和缩略度对大图的缩略度来显示我们的描述器的功效。 我们的实验者展示了图表的精确度, 精确度在精确度上, 精确度的镜微的精确度在精确度上显示。