Denoising deterministic networks using iterative Fourier transforms

Abstract: 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.