We detail a novel Fourier-based approach (IterativeFT) for identifying deterministic network structure in the presence of both edge pruning and Gaussian noise. This technique involves the iterative execution of forward and inverse 2D discrete Fourier transforms on a target network adjacency matrix. The denoising ability of the method is achieved via the application of a sparsification operation to both the real and frequency domain representations of the adjacency matrix with algorithm convergence achieved when the real domain sparsity pattern stabilizes. To demonstrate the effectiveness of the approach, we apply it to noisy versions of several deterministic models including Kautz, lattice, tree and bipartite networks. For contrast, we also evaluate preferential attachment networks to illustrate the behavior on stochastic graphs. We compare the performance of IterativeFT against simple real domain and frequency domain thresholding, reduced rank reconstruction and locally adaptive network sparsification. Relative to the comparison network denoising approaches, the proposed IterativeFT method provides the best overall performance for lattice and Kuatz networks with competitive performance on tree and bipartite networks. Importantly, the InterativeFT technique is effective at both filtering noisy edges and recovering true edges that are missing from the observed network.

翻译：我们详细介绍了一种新颖的基于傅里叶变换的方法（IterativeFT），用于在同时存在边剪枝和高斯噪声的情况下识别确定性网络结构。该技术涉及对目标网络邻接矩阵迭代执行正向和逆向二维离散傅里叶变换。该方法通过将稀疏化操作应用于邻接矩阵的实数域和频域表示来实现去噪能力，当实数域稀疏模式稳定时，算法达到收敛。为证明该方法的有效性，我们将其应用于多个确定性模型的含噪版本，包括Kautz网络、格网、树状网络和二分网络。作为对比，我们还评估了偏好依附网络，以说明其在随机图上的行为。我们将IterativeFT的性能与简单的实数域阈值法、频域阈值法、降秩重构以及局部自适应网络稀疏化方法进行了比较。相对于所比较的网络去噪方法，所提出的IterativeFT方法在格网和Kautz网络上提供了最佳的整体性能，在树状网络和二分网络上也具有竞争力。重要的是，IterativeFT技术在过滤噪声边和恢复观测网络中缺失的真实边方面均表现出色。