# A dictionary learning framework for graphs via filters and optimal transport

arXiv: https://arxiv.org/abs/2609.05919 · HTML: https://mlsanity.com/paper/2609.05919/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Propagation Kernels](https://mlsanity.com/paper/1410.3314/) (2014)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [Gromov-Wasserstein Factorization Models for Graph Clustering](https://mlsanity.com/paper/1911.08530/) (2019)
- [On a linear fused Gromov-Wasserstein distance for graph structured data](https://mlsanity.com/paper/2203.04711/) (2022)
- [Learning subtree pattern importance for Weisfeiler-Lehmanbased graph kernels](https://mlsanity.com/paper/2106.04739/) (2021)
- [FGOT: Graph Distances based on Filters and Optimal Transport](https://mlsanity.com/paper/2109.04442/) (2021)
- [Bures-Wasserstein Means of Graphs](https://mlsanity.com/paper/2305.19738/) (2023)
- [Semi-supervised learning of hierarchical representations of molecules using neural message passing](https://mlsanity.com/paper/1711.10168/) (2017)

## Abstract (arXiv)

We propose a graph dictionary learning (GDL) framework where each graph is represented as a zero-mean Gaussian distribution derived from its filtered Laplacian. Each observed graph is approximated by a barycenter over learned atom graphs, computed under the filter graph distance (fGOT), a graph comparison metric sensitive to global structural properties. The reconstruction error between the observed graph and its barycenter is measured by the surrogate fGOT (sfGOT) distance, a tractable approximation of fGOT that handles graphs without known node correspondence, and is minimized end-to-end via backpropagation. We further provide a novel interpretation of sfGOT through the lens of the Hilbert-Schmidt Independence Criterion, showing that minimizing the sfGOT distance between two graphs is equivalent to maximizing statistical dependence between the spectral embedding of their nodes. Experiments on benchmark datasets demonstrate competitive performance over existing GDL methods on graph clustering and classification tasks.