# Learning heat diffusion graphs

arXiv: https://arxiv.org/abs/1611.01456 · HTML: https://mlsanity.com/paper/1611.01456/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2016.

## Built on by (most cited first, 30 of 39)

- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognition](https://mlsanity.com/paper/2112.03328/) (2021)
- [N2NSkip: Learning Highly Sparse Networks using Neuron-to-Neuron Skip Connections](https://mlsanity.com/paper/2208.03662/) (2022)
- [Representing Molecules as Random Walks Over Interpretable Grammars](https://mlsanity.com/paper/2403.08147/) (2024)
- [Spectro-Riemannian Graph Neural Networks](https://mlsanity.com/paper/2502.00401/) (2025)
- [Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming](https://mlsanity.com/paper/2409.07794/) (2024)
- [Robust Graph Learning Under Wasserstein Uncertainty](https://mlsanity.com/paper/2105.04210/) (2021)
- [Graph Laplacian Learning with Exponential Family Noise](https://mlsanity.com/paper/2306.08201/) (2023)
- [Multiview Graph Learning with Consensus Graph](https://mlsanity.com/paper/2401.13769/) (2024)
- [Learning Cartesian Product Graphs with Laplacian Constraints](https://mlsanity.com/paper/2402.08105/) (2024)
- [Efficient Graph Optimization via Distance-Aware Graph Representation Learning](https://mlsanity.com/paper/2406.17281/) (2024)
- [A Stage-Aware Mixture of Experts Framework for Neurodegenerative Disease Progression Modelling](https://mlsanity.com/paper/2508.07032/) (2025)
- [Skeleton-based Hand-Gesture Recognition with Lightweight Graph Convolutional Networks](https://mlsanity.com/paper/2104.04255/) (2021)
- [Time-varying Graph Learning Under Structured Temporal Priors](https://mlsanity.com/paper/2110.05018/) (2021)
- [Distributed Graph Learning with Smooth Data Priors](https://mlsanity.com/paper/2112.05887/) (2021)
- [Learning Transition Operators From Sparse Space-Time Samples](https://mlsanity.com/paper/2212.00746/) (2022)
- [Online Network Source Optimization with Graph-Kernel MAB](https://mlsanity.com/paper/2307.03641/) (2023)
- [Learning to Identify Graphs from Node Trajectories in Multi-Robot Networks](https://mlsanity.com/paper/2307.04374/) (2023)
- [Piecewise-Stationary Combinatorial Semi-Bandit with Causally Related Rewards](https://mlsanity.com/paper/2307.14138/) (2023)
- [Online Network Inference from Graph-Stationary Signals with Hidden Nodes](https://mlsanity.com/paper/2409.08760/) (2024)
- [Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation](https://mlsanity.com/paper/2411.01567/) (2024)
- [Scalable Hypergraph Structure Learning with Diverse Smoothness Priors](https://mlsanity.com/paper/2504.03583/) (2025)
- [Learning Graph from Smooth Signals under Partial Observation: A Robustness Analysis](https://mlsanity.com/paper/2509.14887/) (2025)
- [Learning Chebyshev Basis in Graph Convolutional Networks for Skeleton-based Action Recognition](https://mlsanity.com/paper/2104.05482/) (2021)
- [Locally Stationary Graph Processes](https://mlsanity.com/paper/2309.01657/) (2023)
- [A Consistent Diffusion-Based Algorithm for Semi-Supervised Graph Learning](https://mlsanity.com/paper/2311.07627/) (2023)
- [Joint Data Inpainting and Graph Learning via Unrolled Neural Networks](https://mlsanity.com/paper/2407.11429/) (2024)
- [Online Proximal ADMM for Graph Learning from Streaming Smooth Signals](https://mlsanity.com/paper/2409.12916/) (2024)
- [Learning Kronecker-Structured Graphs from Smooth Signals](https://mlsanity.com/paper/2505.09822/) (2025)

## Abstract (arXiv)

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the existing works adopt, are often too general and unable to properly capture localized properties of data. In this paper, we go beyond this classical data model and rather propose to represent information as a sparse combination of localized functions that live on a data structure represented by a graph. Based on this model, we focus on the problem of inferring the connectivity that best explains the data samples at different vertices of a graph that is a priori unknown. We concentrate on the case where the observed data is actually the sum of heat diffusion processes, which is a quite common model for data on networks or other irregular structures. We cast a new graph learning problem and solve it with an efficient nonconvex optimization algorithm. Experiments on both synthetic and real world data finally illustrate the benefits of the proposed graph learning framework and confirm that the data structure can be efficiently learned from data observations only. We believe that our algorithm will help solving key questions in diverse application domains such as social and biological network analysis where it is crucial to unveil proper geometry for data understanding and inference.