# Joint Graph and Vertex Importance Learning

arXiv: https://arxiv.org/abs/2303.08552 · HTML: https://mlsanity.com/paper/2303.08552/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [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)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fields](https://mlsanity.com/paper/1404.6640/) (2014)
- [Learning Graphs with Monotone Topology Properties and Multiple Connected Components](https://mlsanity.com/paper/1705.10934/) (2017)
- [Irregularity-Aware Graph Fourier Transforms](https://mlsanity.com/paper/1802.10220/) (2018)
- [Region adaptive graph fourier transform for 3d point clouds](https://mlsanity.com/paper/2003.01866/) (2020)
- [An efficient algorithm for graph Laplacian optimization based on effective resistances](https://mlsanity.com/paper/2004.08451/) (2020)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Two Channel Filter Banks on Arbitrary Graphs with Positive Semi Definite Variation Operators](https://mlsanity.com/paper/2203.02858/) (2022)
- [Perceptually inspired weighted MSE optimization using irregularity-aware graph Fourier transform](https://mlsanity.com/paper/2002.08558/) (2020)
- [Graph Vertex Sampling with Arbitrary Graph Signal Hilbert Spaces](https://mlsanity.com/paper/2002.11238/) (2020)
- [Learning Sparse Graph with Minimax Concave Penalty under Gaussian Markov Random Fields](https://mlsanity.com/paper/2109.08666/) (2021)

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

- [Towards joint graph learning and sampling set selection from data](https://mlsanity.com/paper/2412.09753/) (2024)

## Abstract (arXiv)

In this paper, we explore the topic of graph learning from the perspective of the Irregularity-Aware Graph Fourier Transform, with the goal of learning the graph signal space inner product to better model data. We propose a novel method to learn a graph with smaller edge weight upper bounds compared to combinatorial Laplacian approaches. Experimentally, our approach yields much sparser graphs compared to a combinatorial Laplacian approach, with a more interpretable model.