# Stratified Graph Spectra

arXiv: https://arxiv.org/abs/2201.03696 · HTML: https://mlsanity.com/paper/2201.03696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 85 references that are in the map.
- First posted on arXiv 10 Jan 2022.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification](https://mlsanity.com/paper/1802.08888/) (2018)
- [Dirichlet Graph Variational Autoencoder](https://mlsanity.com/paper/2010.04408/) (2020)
- [Graph Convolutional Network for Recommendation with Low-pass Collaborative Filters](https://mlsanity.com/paper/2006.15516/) (2020)
- [Heat kernel based community detection](https://mlsanity.com/paper/1403.3148/) (2014)
- [Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networks](https://mlsanity.com/paper/2003.11702/) (2020)
- [Signal Recovery on Graphs: Variation Minimization](https://mlsanity.com/paper/1411.7414/) (2014)
- [Non-backtracking spectrum of random graphs: community detection and non-regular Ramanujan graphs](https://mlsanity.com/paper/1501.06087/) (2015)
- [Influence maximization in complex networks through optimal percolation](https://mlsanity.com/paper/1506.08326/) (2015)
- [Distinct types of eigenvector localization in networks](https://mlsanity.com/paper/1505.06024/) (2015)
- [Eigenvector localization in real networks and its implications for epidemic spreading](https://mlsanity.com/paper/1801.05649/) (2018)

## Abstract (arXiv)

In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this definition is not mathematically valid in the cases of vector-valued graph signals which however are typical operands in the state-of-the-art graph learning modeling and analyses. Seeking a generalized transformation decoding the magnitudes of eigencomponents from vector-valued signals is thus the main objective of this paper. Several attempts are explored, and also it is found that performing the transformation at hierarchical levels of adjacency help profile the spectral characteristics of signals more insightfully. The proposed methods are introduced as a new tool assisting on diagnosing and profiling behaviors of graph learning models.