# Online Discriminative Graph Learning from Multi-Class Smooth Signals

arXiv: https://arxiv.org/abs/2101.00184 · HTML: https://mlsanity.com/paper/2101.00184/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2021.

## Built on by (most cited first, 13 of 13)

- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)
- [A Hybrid End-to-End Spatio-Temporal Attention Neural Network with Graph-Smooth Signals for EEG Emotion Recognition](https://mlsanity.com/paper/2307.03068/) (2023)
- [Online Learning Of Expanding Graphs](https://mlsanity.com/paper/2409.08660/) (2024)
- [Network Topology Inference from Smooth Signals Under Partial Observability](https://mlsanity.com/paper/2410.05707/) (2024)
- [Joint Network Topology Inference via Structured Fusion Regularization](https://mlsanity.com/paper/2103.03471/) (2021)
- [Online Graph Learning in Dynamic Environments](https://mlsanity.com/paper/2110.05023/) (2021)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Graph Learning Across Data Silos](https://mlsanity.com/paper/2301.06662/) (2023)
- [Topology Identification and Inference over Graphs](https://mlsanity.com/paper/2512.10183/) (2025)
- [Directed Graph Topology Inference via Graph Filter Identification](https://mlsanity.com/paper/2606.27455/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

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.