Dynamic Network Structure Optimization for Symmetric Non-Negative Matrix Factorization

Network topology is crucial for tasks of network performance analysis, hence we adopt a real-time estimation algorithm to obtain the network topology. We start by spectral decomposing the adjacency matrix corresponding to the network topology (the following is referred to as an adjacency matrix), then estimate the network spectral parameters based on spectral graph theory, and finally synthesize the adjacency matrix using these spectral parameters, while also applying the SNMF (Symmetric Nonnegative Matrix Factorization) algorithm to reduce the estimation error. However, the SNMF algorithm requires the matrix to be sparse, and the lower the rank of the matrix, the lower the algorithm's time complexity. The adjacency matrix of opportunistic networks is often a full-rank matrix; therefore, this paper combines ADMM with gradient projection methods to optimize the network adjacency matrix, resulting in a sparse and low-rank adjacency matrix. Experiments prove that not only does the optimized network significantly reduce the time complexity of SNMF, but it also reduces the error in SNMF.