这篇论文提出了一种新方法，用凸优化来生成带图结构的关联矩阵，比GAN方法更灵活，还做了理论和实验验证。
该论文提出一种基于凸优化的框架，用于生成具有指定图结构稀疏模式的相关矩阵。该方法将初始矩阵投影到正半定约束下的椭圆体（elliptope）上，允许通过控制非对角线元素分布的均值来生成更符合真实数据的矩阵。与基于GAN的方法相比，该框架提供了更高的灵活性和理论保证。实验在神经科学和金融两个真实数据集上验证了方法的有效性。
Graph-Based Correlation Matrix Generation: A Convex Optimization Approach
This work addresses the generation of theoretical correlation matrices with prescribed sparsity patterns associated to graph structures. We propose a novel convex optimization framework in which an initial matrix is projected onto an elliptope under a positive semidefiniteness constraint. Several numerical schemes are implemented and compared. The problem falls within the broader class of matrix completion, where off-diagonal entries corresponding to absent edges are fixed to zero and diagonal entries are fixed to one. Beyond this structural constraint, the approach offers greater flexibility than existing methods by allowing control over the mean of the off-diagonal entry distribution, enabling the generation of correlation matrices that better reflect realistic data. This procedure is not designed to yield a uniform distribution over the feasible set; rather, it provides a principled and tunable way to construct correlation matrices suitable for benchmarking statistical methods for graphical model inference. Theoretical guarantees on the existence of solutions are established, both in the general setting and under the additional mean constraint. Simulation studies illustrate the properties of the generated matrices with respect to graph structure. The methodology is applied to two real-world datasets from neuroscience and finance, and a comparison with GAN-based correlation matrix generation is provided.