In real-world scenarios, it is difficult to know about the complete topology of a huge network with different types of links. In this brief, we propose a method to identify the topology of multidimensional networks from information transmission data. We consider information propagating over edges of a two-dimensional (2D) network, where one type of links is known and the other type is unknown. Given the state of all nodes at each unit time, we can transform the topology identification problem into a compressive sensing framework. A modified reconstruction algorithm, called Sparsity Adaptive Matching Pursuit with Mixed Threshold Mechanism (SAMPMTM), is proposed to tackle the problem. Compared with the classical Sparsity Adaptive Matching Pursuit (SAMP) algorithm, the proposed SAMPMTM algorithm can reduce the conflict rate and improve the accuracy of network recovery. We further demonstrate the performance of this improved algorithm through Monte-Carlo simulations under different network models.
Fast reconstruction algorithm for perturbed compressive sensing based on total least-squares and proximal splitting