Online Discriminative Graph Learning from Multi-Class Smooth Signals

TL;DR

This paper introduces a novel framework for discriminative graph learning from multi-class smooth signals, enabling real-time topology inference in dynamic environments, with applications in graph signal classification.

Contribution

It proposes a new discriminative graph learning method and extends it to dynamic, real-time scenarios using a proximal gradient approach.

Findings

Effective in classifying signals based on learned graphs.

Capable of real-time topology inference in evolving environments.

Validated on synthetic and real datasets.

Abstract

Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification of the relational structures. Graphs are natural descriptors of the relationships between entities of complex environments. The underlying graph is not readily detectable in many cases and one has to infer the topology from the observed signals. Firstly, we address the problem of graph signal classification by proposing a novel framework for discriminative graph learning. To learn discriminative graphs, we invoke the assumption that signals belonging to each class are smooth with respect to the corresponding graph while maintaining non-smoothness with respect to the graphs corresponding to other classes. Secondly, we extend our work to tackle increasingly dynamic environments and real-time topology inference. We develop a proximal gradient (PG) method which can be adapted to situations where the data are acquired on-the-fly. Beyond discrimination, this is the first work that addresses the problem of dynamic graph learning from smooth signals where the sought network alters slowly. The validation of the proposed frameworks is comprehensively investigated using both synthetic and real data.