Awesome Graph Wavelet

Machine Learning Graph Learning
1

Paper

  1. Spectral Wavelet: Wavelets on Graphs via Spectral Graph Theory (citation 1120) [code]
    – SGWT
  2. Spatial Wavelet: INFOCOM 03: Graph Wavelets for Spatial Traffic Analysis (citation 256)
    – CKWT
  3. Deep Wavelet (citation 693)
    – Our goal in this paper is to show that many of the tools of signal processing, adapted Fourier and wavelet analysis can be naturally lifted to the setting of digital data clouds, graphs, and manifolds.
    – https://en.wikipedia.org/wiki/Diffusion_wavelets
    – https://mauromaggioni.duckdns.org/research/#Papers|outline
    – http://helper.ipam.ucla.edu/publications/mgaws5/mgaws5_5164.pdf
  4. ICML 10-Multiscale wavelets on trees, graphs and high dimensional data: theory and applications to semi-supervised learning (citation 205)
    – model data as a tree
  5. Graph Wavelets for Multiscale Community Mining (citation 116)
    – clustering based on SGWT
  6. Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions (citation 66)
  7. NIPS 13-Wavelets on Graphs via Deep Learning (citation 75)
    – lifting scheme, top-down, tree structure
    – cloud point
    – https://www.cnblogs.com/kingoal/archive/2004/04/27/6699.html
  8. Spectral Graph Wavelets and Filter Banks With Low Approximation Error (citation 29)
    – theoretical about wavelet
  9. KDD 18: Learning Structural Node Embeddings via Diffusion Wavelets (citation 79)
    – the characteristic function of the kernel
  10. KDD 16: Graph Wavelets via Sparse Cuts [Extend Version]
    – Haar Wavelet
  11. CVPR 17 workshop: Deep Wavelet Prediction for Image Super-Resolution (citation 59)
    – Haar wavelet
  12. ICLR 19: Graph Wavelet Neural Network
  13. Deep Haar scattering networks (citation 24)
    – Haar Wavelet
  14. Harmonic analysis on directed graphs and applications: from Fourier analysis to wavelets
    – DAG
  15. Learning Sparse Wavelet Representations
    – second generation of wavelet
  16. Parseval wavelets on hierarchical graphs
    – wavelet transform on hierarchical graphs (WTHG)
    – DAG with joint points (DAGJP)
  17. Wavelets on graphs with application to transportation networks
    – abrupt signal along the timeline
  18. NIPS 20 Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks

Wavelet

Perspective

Geometric deep learning: going beyond Euclidean data

Replacing the notion of frequency in time-frequency representations by that of scale leads to wavelet decompositions. Wavelets have been extensively studied in general graph domains [84]. Their objective is to define stable linear decompositions with atoms well-localized both in space and frequency that can efficiently approximate signals with isolated singularities. Similarly to the Euclidean setting, wavelet families can be constructed either from its spectral constraints or from its spatial constraints.
The simplest of such families are Haar wavelets. Several bottom-up wavelet constructions on graphs were studied in [85] and [86]. In [87], the authors developed an unsupervised method that learns wavelet decompositions on graphs by optimizing a sparse reconstruction objective. In [88], ensembles of Haar wavelet decompositions were used to define deep wavelet scattering transforms on general domains, obtaining excellent numerical performance. Learning amounts to finding optimal

Section IV: The Emerging Field of Signal Processing on Graphs [Jouranl Version][Code]