This paper introduces Polynomial Graphical Lasso (PGL), a new approach to
learning graph structures from nodal signals. Our key contribution lies in
modeling the signals as Gaussian and stationary on the graph, enabling the
development of a graph-learning formulation that combines the strengths of
graphical lasso with a more encompassing model. Specifically, we assume that
the precision matrix can take any polynomial form of the sought graph, allowing
for increased flexibility in modeling nodal relationships. Given the resulting
complexity and nonconvexity of the resulting optimization problem, we (i)
propose a low-complexity algorithm that alternates between estimating the graph
and precision matrices, and (ii) characterize its convergence. We evaluate the
performance of PGL through comprehensive numerical simulations using both
synthetic and real data, demonstrating its superiority over several
alternatives. Overall, this approach presents a significant advancement in
graph learning and holds promise for various applications in graph-aware signal
analysis and beyond.

Polynomial Graphical Lasso (PGL) 是一种学习从节点信号中获取图结构的新方法，模拟节点信号为高斯和图上的静态信号，提出了一个结合图融奕和更全面模型的图学习公式，通过估计图和精确度矩阵的低复杂度算法来解决优化问题的复杂性和非凸性，对合成和真实数据进行全面的数值模拟验证其优越性，为图学习提供了重要进展，能在图感知信号分析及其他应用上发挥作用。