# Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification

arXiv: https://arxiv.org/abs/1803.02553 · HTML: https://mlsanity.com/paper/1803.02553/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2018.

## Built on by (most cited first, 18 of 18)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Robust Graph Learning Under Wasserstein Uncertainty](https://mlsanity.com/paper/2105.04210/) (2021)
- [Optimizing k in kNN Graphs with Graph Learning Perspective](https://mlsanity.com/paper/2401.08245/) (2024)
- [Joint Network Topology Inference via Structured Fusion Regularization](https://mlsanity.com/paper/2103.03471/) (2021)
- [MarkovGNN: Graph Neural Networks on Markov Diffusion](https://mlsanity.com/paper/2202.02470/) (2022)
- [Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model](https://mlsanity.com/paper/2203.07831/) (2022)
- [Learning Transition Operators From Sparse Space-Time Samples](https://mlsanity.com/paper/2212.00746/) (2022)
- [Learning Graph Filters for Structure-Function Coupling based Hub Node Identification](https://mlsanity.com/paper/2410.17410/) (2024)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)
- [Statistical Testing on Directed Graphs by Surrogate Data Generation](https://mlsanity.com/paper/2606.00758/) (2026)
- [Diffusion Maps for Signal Filtering in Graph Learning](https://mlsanity.com/paper/2312.14758/) (2023)
- [Joint Data Inpainting and Graph Learning via Unrolled Neural Networks](https://mlsanity.com/paper/2407.11429/) (2024)
- [Sampling Method for Generalized Graph Signals with Pre-selected Vertices via DC Optimization](https://mlsanity.com/paper/2509.14836/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter (a function of graph Laplacian matrices). In order to solve the proposed problem, an algorithm is developed to jointly identify a graph and a graph-based filter (GBF) from multiple signal/data observations. Our algorithm is valid under the assumption that GBFs are one-to-one functions. The proposed approach can be applied to learn diffusion (heat) kernels, which are popular in various fields for modeling diffusion processes. In addition, for specific choices of graph-based filters, the proposed problem reduces to a graph Laplacian estimation problem. Our experimental results demonstrate that the proposed algorithm outperforms the current state-of-the-art methods. We also implement our framework on a real climate dataset for modeling of temperature signals.