Network sparse representation: Decomposition, dimensionality-reduction and reconstruction

Abstract

Network science is a field in which real-world systems are abstracted into complex networks for scientific analysis. Dimensionality reduction for large-scale complex networks to reduce the complexity of problems has become a research focus. In this study, we found that real-world networks are composed of a finite number of atoms through self-replication and superposition. Thus, they can be decomposed into a dictionary and sparse coding. The sparse representation we propose simplifies redundant complex structures and reveals the basis and its representation methods for complex networks. Difficult problems can be solved through this representation, including network similarity metrics, recognition, and reconstruction. Experimental results show that the atoms and sparse coding describe the basic structure and connection pattern of complex networks.