# Spectral Maps for Learning on Subgraphs

arXiv: https://arxiv.org/abs/2205.14938 · HTML: https://mlsanity.com/paper/2205.14938/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 26 of 26)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Subgraph Federated Learning with Missing Neighbor Generation](https://mlsanity.com/paper/2106.13430/) (2021)
- [Distilling Knowledge from Graph Convolutional Networks](https://mlsanity.com/paper/2003.10477/) (2020)
- [Sequential Matching Network: A New Architecture for Multi-turn Response Selection in Retrieval-based Chatbots](https://mlsanity.com/paper/1612.01627/) (2016)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Extract the Knowledge of Graph Neural Networks and Go Beyond it: An Effective Knowledge Distillation Framework](https://mlsanity.com/paper/2103.02885/) (2021)
- [Partial Functional Correspondence](https://mlsanity.com/paper/1506.05274/) (2015)
- [HARP: Hierarchical Representation Learning for Networks](https://mlsanity.com/paper/1706.07845/) (2017)
- [GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding](https://mlsanity.com/paper/1910.02370/) (2019)
- [GCN-Based User Representation Learning for Unifying Robust Recommendation and Fraudster Detection](https://mlsanity.com/paper/2005.10150/) (2020)
- [Label Efficient Semi-Supervised Learning via Graph Filtering](https://mlsanity.com/paper/1901.09993/) (2019)
- [Rewiring with Positional Encodings for Graph Neural Networks](https://mlsanity.com/paper/2201.12674/) (2022)
- [On Self-Distilling Graph Neural Network](https://mlsanity.com/paper/2011.02255/) (2020)
- [MILE: A Multi-Level Framework for Scalable Graph Embedding](https://mlsanity.com/paper/1802.09612/) (2018)
- [Domain Adaptation on Graphs by Learning Aligned Graph Bases](https://mlsanity.com/paper/1803.05288/) (2018)
- [On the optimality of shape and data representation in the spectral domain](https://mlsanity.com/paper/1409.4349/) (2014)
- [A Functional Representation for Graph Matching](https://mlsanity.com/paper/1901.05179/) (2019)
- [GRASP: Graph Alignment through Spectral Signatures](https://mlsanity.com/paper/2106.05729/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Partial Graph Matching via Optimal Partial Transport](https://mlsanity.com/paper/2410.16718/) (2024)
- [Latent Functional Maps: a spectral framework for representation alignment](https://mlsanity.com/paper/2406.14183/) (2024)

## Abstract (arXiv)

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and modified graphs. Classically, these maps are represented as binary node-to-node correspondence matrices and used as-is to transfer node-wise features between the graphs. In this paper, we argue that simply changing this map representation can bring notable benefits to graph learning tasks. Drawing inspiration from recent progress in geometry processing, we introduce a spectral representation for maps that is easy to integrate into existing graph learning models. This spectral representation is a compact and straightforward plug-in replacement and is robust to topological changes of the graphs. Remarkably, the representation exhibits structural properties that make it interpretable, drawing an analogy with recent results on smooth manifolds. We demonstrate the benefits of incorporating spectral maps in graph learning pipelines, addressing scenarios where a node-to-node map is not well defined, or in the absence of exact isomorphism. Our approach bears practical benefits in knowledge distillation and hierarchical learning, where we show comparable or improved performance at a fraction of the computational cost.