论文标题
产品图从具有稀疏性和等级约束的多域数据中学习
Product Graph Learning from Multi-domain Data with Sparsity and Rank Constraints
论文作者
论文摘要
在本文中，我们专注于从多域数据学习产品图。我们假设产品图是由两个较小图的笛卡尔产物形成的，我们称为图因子。我们将产品图学习问题置于估计图因子拉普拉斯矩阵的问题。为了捕获数据中的局部相互作用，我们寻求稀疏图因子并为数据假设平滑度模型。我们提出了一个有效的迭代求解器，用于从数据中学习稀疏产品图。然后，我们将该求解器扩展到将多组分图因子带到产品图聚类中，通过在图形拉普拉斯矩阵上施加等级约束，将其应用于产品图聚类。尽管使用较小的图因子在计算上更具吸引力，但并非所有图形都可以容易地接受精确的笛卡尔产品分解。为此，我们提出了有效的算法，以通过两个较小图的最近的笛卡尔产物近似图。使用有关合成数据和实际数据的几个数值实验证明了开发框架的功效。
In this paper, we focus on learning product graphs from multi-domain data. We assume that the product graph is formed by the Cartesian product of two smaller graphs, which we refer to as graph factors. We pose the product graph learning problem as the problem of estimating the graph factor Laplacian matrices. To capture local interactions in data, we seek sparse graph factors and assume a smoothness model for data. We propose an efficient iterative solver for learning sparse product graphs from data. We then extend this solver to infer multi-component graph factors with applications to product graph clustering by imposing rank constraints on the graph Laplacian matrices. Although working with smaller graph factors is computationally more attractive, not all graphs may readily admit an exact Cartesian product factorization. To this end, we propose efficient algorithms to approximate a graph by a nearest Cartesian product of two smaller graphs. The efficacy of the developed framework is demonstrated using several numerical experiments on synthetic data and real data.
