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
  • Title of Journal : IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS
  • Page Numbers: pp.394-406

Abstract

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.