# A Multiscale Pyramid Transform for Graph Signals

arXiv: https://arxiv.org/abs/1308.4942 · HTML: https://mlsanity.com/paper/1308.4942/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2013.

## Built on by (most cited first, 15 of 15)

- [A Comprehensive Survey on Graph Reduction: Sparsification, Coarsening, and Condensation](https://mlsanity.com/paper/2402.03358/) (2024)
- [Graph Coarsening with Neural Networks](https://mlsanity.com/paper/2102.01350/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph coarsening: From scientific computing to machine learning](https://mlsanity.com/paper/2106.11863/) (2021)
- [Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling](https://mlsanity.com/paper/2402.10634/) (2024)
- [Pyramidal Reservoir Graph Neural Network](https://mlsanity.com/paper/2104.04710/) (2021)
- [A Unified Framework for Optimization-Based Graph Coarsening](https://mlsanity.com/paper/2210.00437/) (2022)
- [Graph Coarsening via Supervised Granular-Ball for Scalable Graph Neural Network Training](https://mlsanity.com/paper/2412.13842/) (2024)
- [Generalizing Downsampling from Regular Data to Graphs](https://mlsanity.com/paper/2208.03523/) (2022)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Spatial-Temporal Tensor Graph Convolutional Network for Traffic Prediction](https://mlsanity.com/paper/2103.06126/) (2021)
- [Identification of vortex in unstructured mesh with graph neural networks](https://mlsanity.com/paper/2311.06557/) (2023)
- [Accelerating local laplacian filters on FPGAs](https://mlsanity.com/paper/2402.12407/) (2024)
- [Sampling Method for Generalized Graph Signals with Pre-selected Vertices via DC Optimization](https://mlsanity.com/paper/2509.14836/) (2025)
- [Hierarchical GNNs for power flow: letting physics shape the hierarchy](https://mlsanity.com/paper/2609.26603/) (2026)

## Abstract (arXiv)

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric structure of the underlying graph data domain. In this paper, we adapt the Laplacian pyramid transform for signals on Euclidean domains so that it can be used to analyze high-dimensional data residing on the vertices of a weighted graph. Our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling, graph reduction, and filtering and interpolation of signals on graphs. Equipped with appropriate notions of these operations, we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs.