# Inhomogeneous graph trend filtering via a l2,0 cardinality penalty

arXiv: https://arxiv.org/abs/2304.05223 · HTML: https://mlsanity.com/paper/2304.05223/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 11 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Trend Filtering on Graphs](https://mlsanity.com/paper/1410.7690/) (2014)
- [Discrete Signal Processing on Graphs: Sampling Theory](https://mlsanity.com/paper/1503.05432/) (2015)
- [Signal Recovery on Graphs: Variation Minimization](https://mlsanity.com/paper/1411.7414/) (2014)
- [Kernel-based Reconstruction of Graph Signals](https://mlsanity.com/paper/1605.07174/) (2016)
- [Vector-Valued Graph Trend Filtering with Non-Convex Penalties](https://mlsanity.com/paper/1905.12692/) (2019)
- [Signal Representations on Graphs: Tools and Applications](https://mlsanity.com/paper/1512.05406/) (2015)

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

- [Sum-of-norms regularized Nonnegative Matrix Factorization](https://mlsanity.com/paper/2407.00706/) (2024)

## Abstract (arXiv)

We study estimation of piecewise smooth signals over a graph. We propose a ℓ2,0-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the nodes. We prove that the proposed GTF model is simultaneously a k-means clustering on the signal over the nodes and a minimum graph cut on the edges of the graph, where the clustering and the cut share the same assignment matrix. We propose two methods to solve the proposed GTF model: a spectral decomposition method and a method based on simulated annealing. In the experiment on synthetic and real-world datasets, we show that the proposed GTF model has a better performances compared with existing approaches on the tasks of denoising, support recovery and semi-supervised classification. We also show that the proposed GTF model can be solved more efficiently than existing models for the dataset with a large edge set.