Spatio-Temporal-Graph-Convolutional-Networks-A-Deep-Learning-Framework-for-Traffic-Forecasting

reference

• https://www.zhihu.com/question/54504471
• https://en.wikipedia.org/wiki/Laplacian_matrix
• https://tkipf.github.io/graph-convolutional-networks/
• https://www.inference.vc/how-powerful-are-graph-convolutions-review-of-kipf-welling-2016-2/
• http://cs229.stanford.edu/section/cs229-moregaussians.pdf

abstract

• Spatio-Temporal Graph Convolutional Network
• tackle the time series prediction problem in traffic domain
• complete convolutional structures.

introduction

• linear regression perform well on short interval forecast instead of long terms
• this is a data-driven and using spotio-temporal information method.
• fully utilize spatio-information instead of treating it as discrete units
• $$\hat v_{t+1},...,\hat v_{t+H} = argmax log_{10} P(v_{t+1},...,v_{t+H}|v_{t-M},...,v_{t})$$
• 
• where $$v_t \in R^n$$, n is an observation vector of n road segments at time step t

Convolutions on Graphs

• normalized Laplacian

  • Random walk normalized Laplacian
  • analogy to The Multivariate Gaussian Distribution
  • Symmetric normalized Laplacian L:

• first generation of GNC

• second generation of GNC

  • if k == n, receptive field is n hop

• third generation of GNC

  • where $$c_1$$, $$c_2$$ and $$c_3$$ are fixed
  • The only trainable parameters are $$\theta_0$$ and $$\theta_1$$
  • in the final version the authors even further fix $$\theta_0 = -\theta_1$$

Network Architecture

• main architecture
• GLU architecture
• main equation
• final equation

Experiments

• linear interpolation method for missing values
• normalized by standard score method((x-mean)/std)
• adjacency matrix 10,0.5

result