论文标题
核心外围结构图的生成模型和学习算法
Generative Models and Learning Algorithms for Core-Periphery Structured Graphs
论文作者
论文摘要
我们认为核心外围结构图，它们分别具有一组密集和稀疏连接的节点的图，称为核心和周围节点。节点的所谓核心分数与它是核心节点的可能性有关。在本文中，我们专注于从其节点属性和连接结构中学习图的核心分数。为此，我们提出了两类概率图形模型：仿射和非线性。首先，我们描述了仿射生成模型，以建模节点属性对其核心分数的依赖性，从而确定图形结构。接下来，我们讨论非线性生成模型，其中节点属性的部分相关通过潜在的核心分数影响图形结构。当图形结构和节点属性都可用时，我们开发了用于推断图形参数和核心分数的算法。当只有图形的节点属性可用时，我们会共同学习核心 - 外围结构图及其核心分数。我们提供了几个合成和现实数据集的数值实验的结果，以证明开发模型和算法的功效。
We consider core-periphery structured graphs, which are graphs with a group of densely and sparsely connected nodes, respectively, referred to as core and periphery nodes. The so-called core score of a node is related to the likelihood of it being a core node. In this paper, we focus on learning the core scores of a graph from its node attributes and connectivity structure. To this end, we propose two classes of probabilistic graphical models: affine and nonlinear. First, we describe affine generative models to model the dependence of node attributes on its core scores, which determine the graph structure. Next, we discuss nonlinear generative models in which the partial correlations of node attributes influence the graph structure through latent core scores. We develop algorithms for inferring the model parameters and core scores of a graph when both the graph structure and node attributes are available. When only the node attributes of graphs are available, we jointly learn a core-periphery structured graph and its core scores. We provide results from numerical experiments on several synthetic and real-world datasets to demonstrate the efficacy of the developed models and algorithms.
