超球面空间中复杂网络的机器学习分析
Machine Learning Analysis of Complex Networks in Hyperspherical Space
摘要：
复杂网络是一个复杂系统的关系拓扑结构的浓缩表示。这种网络存在的一个主要原因是通过这些复杂系统的实体进行项目传输。在这里，我们考虑一个可通信性函数，该函数说明了物品在网络上流动的路线。这样一个函数将网络自然地嵌入到一个欧氏高维球面中。我们使用这种嵌入的几何参数之一，即超球面中节点位置向量之间的角度，从网络中提取结构信息。这些信息是通过使用机器学习技术提取的，例如非度量多维缩放和K均值聚类算法。第一个允许我们将可通信性超球体的维度减少到允许网络可视化的三维。第二个允许集群的网络节点的基础上，他们的相似之处，他们的能力，成功地通过网络传递信息。在基准网络中测试这些方法并将其与网络中最常用的聚类方法进行比较后，我们分析了两个真实世界的例子。在第一个，由一个引用网络，我们发现引用组，反映了他们的出版物中使用的数学水平。在第二部分中，我们发现了共同参与人类疾病的基因组，报告了一些共同参与癌症和其他疾病的基因。这两个例子都强调了当前方法在发现关系数据新模式方面的潜力。
英文摘要：
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here, we consider a communicability function that accounts for the routes through which items flow on networks. Such a function induces a natural embedding of a network in a Euclidean high-dimensional sphere. We use one of the geometric parameters of this embedding, namely the angle between the position vectors of the nodes in the hyperspheres, to extract structural information from networks. Such information is extracted by using machine learning techniques, such as nonmetric multidimensional scaling and K-means clustering algorithms. The first allows us to reduce the dimensionality of the communicability hyperspheres to 3-dimensional ones that allow network visualization. The second permits to cluster the nodes of the networks based on their similarities in terms of their capacity to successfully deliver information through the network. After testing these approaches in benchmark networks and compare them with the most used clustering methods in networks we analyze two real-world examples. In the first, consisting of a citation network, we discover citation groups that reflect the level of mathematics used in their publications. In the second, we discover groups of genes that coparticipate in human diseases, reporting a few genes that coparticipate in cancer and other diseases. Both examples emphasize the potential of the current methodology for the discovery of new patterns in relational data.
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