Mask Combination of Multi-Layer Graphs for Global Structure Inference

Bayram E., Thanou D., VURAL E. , Frossard P.

IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, vol.6, pp.394-406, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6
  • Publication Date: 2020
  • Doi Number: 10.1109/tsipn.2020.2995515
  • Page Numbers: pp.394-406
  • Keywords: Task analysis, Social network services, Semisupervised learning, Signal representation, Data analysis, Laplace equations, Information processing, Multi-relational networks, multi-view data analysis, network data analysis, graph signal processing, structure inference, link prediction, graph learning, PRECISION MATRIX, NETWORK


Structure inference is an important task for network data processing and analysis in data science. In recent years, quite a few approaches have been developed to learn the graph structure underlying a set of observations captured in a data space. Although real-world data is often acquired in settings where relationships are influenced by a priori known rules, such domain knowledge is still not well exploited in structure inference problems. In this paper, we identify the structure of signals defined in a data space whose inner relationships are encoded by multi-layer graphs. We aim at properly exploiting the information originating from each layer to infer the global structure underlying the signals. We thus present a novel method for combining the multiple graphs into a global graph using mask matrices, which are estimated through an optimization problem that accommodates the multi-layer graph information and a signal representation model. The proposed mask combination method also estimates the contribution of each graph layer in the structure of signals. The experiments conducted both on synthetic and real-world data suggest that integrating the multi-layer graph representation of the data in the structure inference framework enhances the learning procedure considerably by adapting to the quality and the quantity of the input data.