# Adaptive Diffusions for Scalable Learning over Graphs

arXiv: https://arxiv.org/abs/1804.02081 · HTML: https://mlsanity.com/paper/1804.02081/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2018.

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

- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Improving Graph Neural Networks with Simple Architecture Design](https://mlsanity.com/paper/2105.07634/) (2021)
- [Graph filtering over expanding graphs](https://mlsanity.com/paper/2203.08058/) (2022)
- [Multiple Kernel Representation Learning on Networks](https://mlsanity.com/paper/2106.05057/) (2021)
- [Learning Optimal Graph Filters for Clustering of Attributed Graphs](https://mlsanity.com/paper/2211.04634/) (2022)
- [Online Graph Filtering Over Expanding Graphs](https://mlsanity.com/paper/2409.07204/) (2024)
- [Scale-aware Message Passing For Graph Node Classification](https://mlsanity.com/paper/2411.19392/) (2024)
- [FairRARI: A Plug and Play Framework for Fairness-Aware PageRank](https://mlsanity.com/paper/2602.08589/) (2026)
- [ScaleNet: Scale Invariance Learning in Directed Graphs](https://mlsanity.com/paper/2411.08758/) (2024)
- [Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size](https://mlsanity.com/paper/2510.04440/) (2025)
- [Stochastic Sequential Decision Making over Expanding Networks with Graph Filtering](https://mlsanity.com/paper/2603.19501/) (2026)

## Abstract (arXiv)

Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which the chosen diffusion captures a typically unknown label propagation mechanism, that can be specific to the underlying graph, and potentially different for each class. The present work introduces a disciplined, data-efficient approach to learning class-specific diffusion functions adapted to the underlying network topology. The novel learning approach leverages the notion of "landing probabilities" of class-specific random walks, which can be computed efficiently, thereby ensuring scalability to large graphs. This is supported by rigorous analysis of the properties of the model as well as the proposed algorithms. Furthermore, a robust version of the classifier facilitates learning even in noisy environments. Classification tests on real networks demonstrate that adapting the diffusion function to the given graph and observed labels, significantly improves the performance over fixed diffusions; reaching -- and many times surpassing -- the classification accuracy of computationally heavier state-of-the-art competing methods, that rely on node embeddings and deep neural networks.