Graph Signals and Graph Signal Processing

Data

subject:: Data Science Methods for Large Scale Graphs

Some extra notes of GSO : here
graph convolutions

File status type Lectures
normalized graph laplacian complete 💡
normalized adjacency matrix complete 💡
network diffusion process complete 💡
neighborhood (graph) complete 💡
graph complete 💡
graph signals complete 💡
graph shift operator complete 💡
graph laplacian empty 💡
degree matrix complete 💡
adjacency matrix complete 💡
random walk laplacian complete 💡
random walk matrix complete 💡
undirected graph complete 💡
unweighted graph complete 💡
interpretation of the graph laplacian complete 💡
    graph fourier transform complete 💡
    interpretation of the symmetric graph laplacian complete 💡
    symmetric laplacian complete 💡
    total variation energy complete 💡
    linear graph filter complete 💡
    inverse graph fourier transform complete 💡
    graph convolution complete 💡
    convolutional graph filters are shift equivariant complete 🧮
    convolutional graph filters are permutation equivariant complete 🧮
    convolutional graph filters are local complete 🧮
    conditions for finding a convolutional graph filter complete 🧮
    spectral representation of a convolutional graph filter complete 💡
    the spectral representation of a graph filter is independent from the graph complete 💡
    the spectral graph filter operates on a signal pointwise complete 🧮
    analytic function complete 💡
    Empirical risk minimization problem empty 💡
    node-level task complete 💡
    inductive learning complete 💡
    hypothesis class complete 💡
    graph-level problem complete 💡
    graph signal processing problem complete 💡
    approximation of heaviside functions using convolutional graph filters empty 🧮
    spectral graph filter complete 💡
    statistical risk minimization problem complete 💡
    supervised learning empty 💡
    we can represent any analytic function with convolutional graph filters complete 🧮
    multi-layer graph perceptron complete 💡
    graph perceptron complete 💡
    convolutional filter bank complete 💡
    Graph Neural Networks complete 💡
    balanced stochastic block model complete 💡
    almost exact recovery complete 💡
    almost exact recovery is impossible when the signal to noise ratio is less than the threshold complete 🧮
    signal to noise ratio complete 💡
    spectral clustering empty 💡
    stochastic block model complete 💡
    unsupervised empty 💡
    information theoretic threshold complete 💡
    feature-aware spectral embeddings complete 💡
    coordinate representation complete 💡
    contextual stochastic block model empty 💡
    compressed sparse row representation complete 💡
    sometimes spectral algorithms fail complete 💡
    spectral embedding complete 💡
    we can use GNNs to solve feature-aware semi-supervised learning problems complete 💡
    message passing neural network complete 💡
    MPNNs can be expressed as graph convolutions complete 💡
    leaky ReLU complete 💡
    graph attention model complete 💡
    fully connected readout layer complete 💡
    readout layer complete 💡
    graph convolutional network complete 💡
    graph SAGE complete 💡
    chebyshev polynomials are orthogonal complete 💡
    chebyshev equioscillation theorem complete 🧮
    GCN layers can be written as graph convolutions complete 💡
    graph isomorphism complete 💡
    color refinement algorithm in progress 💡
    aggregation readout layer complete 💡
    Weisfeiler-Leman Graph Isomorphism Test in progress 💡
    We can verify whether graphs without node features and different laplacian eigenvalues are not isomorphic complete 🧮
    graph isomorphism is not solvable in polynomial time complete 💡
      graph homomorphism complete 💡
      computational graph complete 💡
      Graph Isomorphism Network complete 💡
      GINs are maximally powerful for anonymous input graphs complete 💡
      homomorphism density complete 💡
      cycle homomorphism density is given by the trace of the adjacency matrix complete 💡
      random graphs in a gin are good for graph isomorphism complete 💡
      quasi-symmetry complete 💡
      operator distance modulo permutations complete
      operator dilation complete 💡
      graph convolutions are stable to perturbations in the data and coefficients complete 💡
      graph automorphism complete 💡
      Lipschitz continuous complete 💡
      integral lipschitz filters are stable to dilations complete 🧮
      integral Lipschitz filter complete 💡
      filter permutation invariance complete 💡
      eigenvector misalignment complete 💡
      discriminability of a graph filter in progress 💡
      Lipschitz filters are stable to additive perturbations complete 🧮
      relative perturbation edge changes are tied to node degree complete 💡
      relative perturbations complete 💡
      stability and size tradeoff for realistic sparsity pattern considerations setting in progress 💡
      stability-discriminability tradeoff for Lipschitz filters complete 💡
      stable graph filter complete 💡
      GNNs perform better than their constituent filters complete 💡
      GNNs inherit stability from their layers complete 🧮