Mask Combination of Multi-layer Graphs for Global Structure Inference

TL;DR

This paper introduces a novel method for combining multi-layer graphs using mask matrices to improve global structure inference in network data analysis, effectively leveraging domain knowledge and multi-layer information.

Contribution

It proposes a new mask-based graph combination approach that optimally integrates multi-layer graphs for better structure inference, estimating each layer's contribution.

Findings

Enhanced structure inference accuracy on synthetic data.

Improved results on real-world datasets.

Adaptive integration of multi-layer information benefits learning.

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.