# Graph Learning from Data under Structural and Laplacian Constraints

arXiv: https://arxiv.org/abs/1611.05181 · HTML: https://mlsanity.com/paper/1611.05181/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2016.

## Built on by (most cited first, 8 of 8)

- [Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognition](https://mlsanity.com/paper/2112.03328/) (2021)
- [A Computational Framework for Modeling Complex Sensor Network Data Using Graph Signal Processing and Graph Neural Networks in Structural Health Monitoring](https://mlsanity.com/paper/2105.05316/) (2021)
- [Joint Signal Recovery and Graph Learning from Incomplete Time-Series](https://mlsanity.com/paper/2312.16940/) (2023)
- [Skeleton-based Hand-Gesture Recognition with Lightweight Graph Convolutional Networks](https://mlsanity.com/paper/2104.04255/) (2021)
- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)
- [Learning Chebyshev Basis in Graph Convolutional Networks for Skeleton-based Action Recognition](https://mlsanity.com/paper/2104.05482/) (2021)
- [Cramer-Rao Bounds for Laplacian Matrix Estimation](https://mlsanity.com/paper/2504.04576/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i) formulation of various graph learning problems, (ii) their probabilistic interpretations and (iii) associated algorithms. Specifically, graph learning problems are posed as estimation of graph Laplacian matrices from some observed data under given structural constraints (e.g., graph connectivity and sparsity level). From a probabilistic perspective, the problems of interest correspond to maximum a posteriori (MAP) parameter estimation of Gaussian-Markov random field (GMRF) models, whose precision (inverse covariance) is a graph Laplacian matrix. For the proposed graph learning problems, specialized algorithms are developed by incorporating the graph Laplacian and structural constraints. The experimental results demonstrate that the proposed algorithms outperform the current state-of-the-art methods in terms of accuracy and computational efficiency.