Large-scale graph signal denoising: A heuristic approach

Graph signal denoising aims to extract a clean signal from a noisy graph while preserving its intrinsic structure, which is particularly challenging in large-scale graphs. This study presents an efficient method utilizing spectral kernels to create a dictionary of atoms within the graph spectrum and applies analysis coefficients to Stein's unbiased risk estimator (SURE) for denoising. Given the computational difficulty of exhaustive search on large-scale graphs, we enhance this process with spectral clustering for parallel processing and the Imperialist competitive algorithm (ICA) for the search strategy. Our approach divides the initial graph using spectral clustering into k-clusters via the first k-eigenvectors of the graph Laplacian matrix with the k-means algorithm, then applies the SURE scheme to each cluster separately. ICA optimizes the search within each cluster. Results indicate that independently applying SURE and ICA to each subgraph, combined with parallel processing, significantly reduces computational complexity compared to processing the entire graph. This efficiency gain is due to easier parallel processing of subgraphs and more effective ICA execution. Finally, we aggregate the denoised signals from different subgraphs into a unified denoised signal, minimizing mean square error (MSE). Extensive evaluation of various graphs demonstrates the scheme's effectiveness, especially on large graphs.