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Project - Evaluation:

Experiments

Operators:

• SGC (l + nl), GC (l + nl), AGC, ASGC, ASGCP, GlobalSLC

Hyperparameters:

• batch-size: 16
• bottleneck-channels: 128
• spatial-channels: 96
• dropout: 0.1
• dropout-att: 0.5 (TBD)
• forecast-horizon: 3, 6 separately

Datasets:

• METR-LA
• PEMS-BAY

Report Outline

Introduction:

• Context
  • Spatio-temporal learning traffic networks
  • Inter- & Intra- series correlation; link this to spatial and temporal correlations/dependencies
  • ARIMA -(highly non linear dynamics & inter-series correlations)-> GNNs --> GNNs that learn graph structure
  • Inter series correlation:
    • prior graph based on road; connected (by roads) Nodes influence each other
    • learned based on patterns in data (not expressed the road network)
• Issue
  • Misrepresentation of capabilities of certain mechanisms
• Problem
  • Zhang et al. and Chao et al. do both learn laplacian; but with different mechanisms and the impact these mechanisms have is not clear
• Others
  • Usually they to propose Ablation studies to show effectiveness
  • Compare their Architecture to competing architectures
  • Only whole architectures are compared & not components
  • Effectiveness of components is only shown in own temporal model
    • TODO: find out how temporal modeling is done in Chao et al. (maybe with DFT)
• Novelty
  • Contrast to others
  • Experiment with convolutions in fixed temporal framework
  • Compare components rather than models
• Challenges
  • Temporal modeling --> Main cause for lack in performance convolution operations have a fixed math. definition and therefore require no engineering or tuning. If implemented correctly there is nothing to tune about conv. operators.
  • Structuring 8 convolution kernels;
• Approach
  • Similarly as in abstract
• Contributions
  • list all novel implementations: GC-l, ASGCP, ASGC, AGC
  • one sentence reffering to repo --> gives one place for all implementation

Scenario:

• Benefits from our approach:
• Insight on which mechanisms for learning a graph structure might be well suited for spatial modelling; without discussing temporal modelling
• For example: researchers know how to build their convolution kernels for spatio-temporal problems
• Central GitHub repo for lots of kernels and temporal models.
• Dataset:
• Descriptive metrics; #Sensors (Nodes), time-frame (e.g. aggregated over 5 min intervals), Time-Frame (Mar 1st 2012 - Jun 30th 2012), Caltrans PeMS (Performance Measuring System)
• Features: Signal (Mph), Timestamp (Cyclical) over 1 day

Preliminaries:

• Graph Convolution Spatial vs. Spectral on a high-level and some history (Kipf & Welling)
• Spatial Convolution (GC)
• Spectral Convolution (SGC)
• Structure Learning with Parameters Zhang et al. combine SLCs which do learn global and local graph representations. State that we only cover Global view and not local view.
• Define spectral convolution with learnable laplacian (GC-l, SGC-l)
• Latent Correlation Layer Explain Attention mechanism on a high level.
• Define spectral and spatial convolution kernels (AGC, ASGC)
• Combinations
• Global SLC
• ASGCP
• Temporal Model (image of P3D with substitutable Graph Convolution)
• Table with all Kernels listed.

Threats to validity: (Ask Chris for Feedback)

• External Validity
• Only tested on Traffic Prediction (based on speed readings)
• Model might not generalize for different types of road (inner city vs highway, big city vs small city).
• Long forecast horizons not tested
• Same country
• Internal Validity
• Hyperparameter tuning on Val Dataset
• Structure Learning vs. #Parameters
• Construct Validity
• RMSE vs MAE vs MAPE; these are all valid in traffic forecasting;
• Conclusion Validity
• Confirm not prove;
• Performance P3D not in general
• Avoid by having at least 2 samples for each concept
• 2 Datasets