StemGNN

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#graph neural network #graph #forecasting #time series
  • What problem is StemGNN solving:
    • intra-series temporal pattern: DFT
      • Each series
    • inter-series correlations
      • At each step, the interactions between nodes
      • reversible operator
    • Example problem
      • Covid cases: DE, AT, NL, …
      • Predicting each country without considering the interactions between them
      • Or introduce the people flow between them
  • GFT:
    • Completes DFT as it takes care of the inter-series correlations
    • one extra slide for this topic
  • Convolutions on Graphs
    • one extra slide for this topic

Graph Basics

How to build the graph

  • “self-attention”:
    • outer product of key, query, as the adjacency matrix
      • key, query are of length # of ndoes

Weights and Biases

  • LC
  • 1DConv
  • GLU
  • FC

Experiments

  • Traffic adjacency matrix
    • neighbouring sensors have higher correlations
  • Covid
    • Neighbouring countries have higher correlation
    • Spetral analysis:
      • Some eigenvectors have clear meanings

Week spots

Architecture

stateDiagram-v2 with_spectral_matrix_representation: Spectral Matrix Representation with_temporal_patterns_in_freq_domain: Temporal Patterns in Frequency Domain with_latent_correlation: Latent Correlation Representation dft_repr: Discrete Fourier Transformed Representation conv_dft_repr: Convolved DFT Representation [*] --> with_latent_correlation: Latent Correlation Layer with_latent_correlation --> with_latent_correlation state with_latent_correlation { state with_spectral_matrix_representation { [*] --> dft_repr: Discrete Fourier Transform dft_repr --> conv_dft_repr: 1DConv conv_dft_repr --> gated_conv_dft_repr: Gated Linear Unit gated_conv_dft_repr --> inverse_dft_gated_conv_dft_repr: IDFT } [*] --> with_spectral_matrix_representation: Graph Fourier Transform note right of with_spectral_matrix_representation: This happens in Spe-Seq Cell with_spectral_matrix_representation --> with_temporal_patterns_in_freq_domain with_temporal_patterns_in_freq_domain --> with_conv_temporal_patterns: Graph Convolution with_conv_temporal_patterns --> with_timeseries_restored: IGFT with_timeseries_restored --> Forecast with_timeseries_restored --> Backcast } note right of with_latent_correlation: This is done in StemGNN Block with_latent_correlation --> [*]

Planted: by ;

References:
  1. Cao D, Wang Y, Duan J, Zhang C, Zhu X, Huang C, et al. Spectral Temporal Graph Neural Network for multivariate time-series forecasting. arXiv [cs.LG]. 2021. Available: http://arxiv.org/abs/2103.07719
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Lei Ma (2022). 'StemGNN', Datumorphism, 01 April. Available at: https://datumorphism.leima.is/reading/stemgnn/.