# Mask Combination of Multi-layer Graphs for Global Structure Inference

arXiv: https://arxiv.org/abs/1910.10114 · HTML: https://mlsanity.com/paper/1910.10114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Unveiling Anomalous Edges and Nominal Connectivity of Attributed Networks](https://mlsanity.com/paper/2104.08637/) (2021)

## Abstract (arXiv)

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.