• 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

## How to build the graph

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

• LC
• 1DConv
• GLU
• FC

## Experiments

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

## 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 ;

Lei Ma (2022). 'StemGNN', Datumorphism, 01 April. Available at: https://datumorphism.leima.is/reading/stemgnn/.