# Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals

arXiv: https://arxiv.org/abs/2310.19005 · HTML: https://mlsanity.com/paper/2310.19005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 29 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Identifying the Topology of Undirected Networks from Diffused Non-stationary Graph Signals](https://mlsanity.com/paper/1801.03862/) (2018)
- [Kernel-based Graph Learning from Smooth Signals: A Functional Viewpoint](https://mlsanity.com/paper/2008.10065/) (2020)
- [Graph Laplacian mixture model](https://mlsanity.com/paper/1810.10053/) (2018)
- [Localized Iterative Methods for Interpolation in Graph Structured Data](https://mlsanity.com/paper/1310.2646/) (2013)
- [Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals](https://mlsanity.com/paper/2202.02815/) (2022)

## Abstract (arXiv)

Within the context of Graph Signal Processing (GSP), Graph Learning (GL) is concerned with the inference of the graph's underlying structure from nodal observations. However, real-world data often contains diverse information, necessitating the simultaneous clustering and learning of multiple graphs. In practical applications, valuable node-specific covariates, represented as kernels, have been underutilized by existing graph signal clustering methods. In this letter, we propose a new framework, named Kernel-based joint Multiple GL and clustering of graph signals (KMGL), that leverages a multi-convex optimization approach. This allows us to integrate node-side information, construct low-pass filters, and efficiently solve the optimization problem. The experiments demonstrate that KMGL significantly enhances the robustness of GL and clustering, particularly in scenarios with high noise levels and a substantial number of clusters. These findings underscore the potential of KMGL for improving the performance of GSP methods in diverse, real-world applications.