# Learning parametric dictionaries for graph signals

arXiv: https://arxiv.org/abs/1401.0887 · HTML: https://mlsanity.com/paper/1401.0887/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2014.

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

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Restructuring Graph for Higher Homophily via Adaptive Spectral Clustering](https://mlsanity.com/paper/2206.02386/) (2022)
- [Graph filtering over expanding graphs](https://mlsanity.com/paper/2203.08058/) (2022)
- [Message Passing in Graph Convolution Networks via Adaptive Filter Banks](https://mlsanity.com/paper/2106.09910/) (2021)
- [Topological Dictionary Learning](https://mlsanity.com/paper/2503.11470/) (2025)
- [Feature Expansion for Graph Neural Networks](https://mlsanity.com/paper/2305.06142/) (2023)
- [Online Network Source Optimization with Graph-Kernel MAB](https://mlsanity.com/paper/2307.03641/) (2023)
- [Efficient Matrix Factorization Via Householder Reflections](https://mlsanity.com/paper/2405.07649/) (2024)
- [Fast Structured Orthogonal Dictionary Learning using Householder Reflections](https://mlsanity.com/paper/2409.09138/) (2024)
- [Multi-Output Gaussian Processes for Graph-Structured Data](https://mlsanity.com/paper/2505.16755/) (2025)
- [Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering](https://mlsanity.com/paper/2511.16111/) (2025)
- [Learning fMRI activations dictionaries across individual geometries via optimal transport](https://mlsanity.com/paper/2605.20883/) (2026)

## Abstract (arXiv)

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification.