# Learning Sparse Graphs via Majorization-Minimization for Smooth Node Signals

arXiv: https://arxiv.org/abs/2202.02815 · HTML: https://mlsanity.com/paper/2202.02815/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 6 Feb 2022.

## Builds on (most cited first, 8 of 8)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Structured Graph Learning for Clustering and Semi-supervised Classification](https://mlsanity.com/paper/2008.13429/) (2020)
- [Accelerated Graph Learning from Smooth Signals](https://mlsanity.com/paper/2110.09677/) (2021)
- [Online Graph Learning under Smoothness Priors](https://mlsanity.com/paper/2103.03762/) (2021)

## Built on by (most cited first, 4 of 4)

- [Graph Structure Learning with Interpretable Bayesian Neural Networks](https://mlsanity.com/paper/2406.14786/) (2024)
- [Kernel-based Joint Multiple Graph Learning and Clustering of Graph Signals](https://mlsanity.com/paper/2310.19005/) (2023)
- [Learning Time-Varying Graphs from Incomplete Graph Signals](https://mlsanity.com/paper/2510.17903/) (2025)
- [Learning Superpixel Ensemble and Hierarchy Graphs for Melanoma Detection](https://mlsanity.com/paper/2604.03710/) (2026)

## Abstract (arXiv)

In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the principle of majorization-minimization (MM), wherein we first obtain a tight surrogate function for the graph learning objective and then solve the resultant surrogate problem which has a simple closed form solution. The proposed algorithm does not require tuning of any hyperparameter and it has the desirable feature of eliminating the inactive variables in the course of the iterations - which can help speeding up the algorithm. The numerical simulations conducted using both synthetic and real world (brain-network) data show that the proposed algorithm converges faster, in terms of the average number of iterations, than several existing methods in the literature.