论文标题
通过大量最小化学习稀疏图，以获得光滑的节点信号
Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals
论文作者
论文摘要
在这封信中，我们提出了一种通过估算其邻接矩阵来学习稀疏加权图的算法，假设观察到的信号在图表的节点上平稳变化。所提出的算法基于大型化最小化（MM）的原理，其中我们首先获得了图形学习目标的紧密替代功能，然后解决所得的替代问题，该问题具有简单的封闭形式解决方案。所提出的算法不需要对任何超参数进行调整，并且具有可取的特征，即在迭代过程中消除非活性变量 - 这可以帮助加快算法加速。使用合成世界和现实世界（脑网络）进行进行的数值模拟表明，与文献中的几种现有方法相比，所提出的算法收敛的速度比平均迭代次数更快。
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the principle of majorization-minimization (MM), wherein we first obtain a tight surrogate function for the graph learning objective and then solve the resultant surrogate problem which has a simple closed form solution. The proposed algorithm does not require tuning of any hyperparameter and it has the desirable feature of eliminating the inactive variables in the course of the iterations - which can help speeding up the algorithm. The numerical simulations conducted using both synthetic and real world (brain-network) data show that the proposed algorithm converges faster, in terms of the average number of iterations, than several existing methods in the literature.
