# Signal Representations on Graphs: Tools and Applications

arXiv: https://arxiv.org/abs/1512.05406 · HTML: https://mlsanity.com/paper/1512.05406/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2015.

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

- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Inhomogeneous graph trend filtering via a l2,0 cardinality penalty](https://mlsanity.com/paper/2304.05223/) (2023)
- [Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering](https://mlsanity.com/paper/2511.16111/) (2025)
- [Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification](https://mlsanity.com/paper/2610.19351/) (2026)

## Abstract (arXiv)

We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For each class, we provide an explicit definition of the graph signals and construct a corresponding graph dictionary with desirable properties. We then study how such graph dictionary works in two standard tasks: approximation and sampling followed with recovery, both from theoretical as well as algorithmic perspectives. Finally, for each class, we present a case study of a real-world problem by using the proposed methodology.