# Vector-Valued Graph Trend Filtering with Non-Convex Penalties

arXiv: https://arxiv.org/abs/1905.12692 · HTML: https://mlsanity.com/paper/1905.12692/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 12 of 12)

- [Elastic Graph Neural Networks](https://mlsanity.com/paper/2107.06996/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Chasing Fairness in Graphs: A GNN Architecture Perspective](https://mlsanity.com/paper/2312.12369/) (2023)
- [Robust Graph Neural Networks via Unbiased Aggregation](https://mlsanity.com/paper/2311.14934/) (2023)
- [Clustered Federated Learning via Generalized Total Variation Minimization](https://mlsanity.com/paper/2105.12769/) (2021)
- [Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties](https://mlsanity.com/paper/2309.03094/) (2023)
- [Plug In and Learn: Federated Intelligence over a Smart Grid of Models](https://mlsanity.com/paper/2302.04363/) (2023)
- [Inhomogeneous graph trend filtering via a l2,0 cardinality penalty](https://mlsanity.com/paper/2304.05223/) (2023)
- [Learning Multi-Attribute Differential Graphs with Non-Convex Penalties](https://mlsanity.com/paper/2505.09748/) (2025)
- [Federated Smoothing Proximal Gradient for Quantile Regression with Non-Convex Penalties](https://mlsanity.com/paper/2408.05640/) (2024)
- [Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling](https://mlsanity.com/paper/2608.01318/) (2026)
- [Graph-dependent shrinkage priors for Bayesian trend filtering](https://mlsanity.com/paper/2608.23802/) (2026)

## Abstract (arXiv)

This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.