Balanced Graph Structure Learning for MTS Forecasting (2022)Permalink

ContentsPermalink

  1. Abstract
  2. Introduction
  3. Graph Structure Learning
  4. Methodology
    1. Graph Structure Learning module
      1. MGN
      2. SSU
    2. Temporal Forecasting module
      1. Graph Selection
      2. DCRNN


0. AbstractPermalink

Propose

  • without the need of pre-defined graphs

  • balance the trade-off between efficiency & flexibility


BGSLF (Baalnced Graph Structure Learning for MTS Forecasting)Permalink

Modules

  • (1) MGN (Multi-Graph Generation Network)
  • (2) Graph Selection Module
    • (1) & (2) to balance the trade-off
  • (3) SSU (Smooth Sparse Unit)
    • to design sparse graph structure


1. IntroductionPermalink

ContributionsPermalink

  1. Propose BGSLF

    • aim of learning smooth & sparse dependencies between variables
    • can generate a specified number of graphs
    • then, can select BEST graph per input
  2. Graph Structure Learning module

    • incorporate domain knowledge

      save lots of parameters

  3. SSU (Smooth Sparse Unit)

    • to infer continuous & sparse dependencies
    • no need of non-differentiable functions
      • ex) Top-K, Regularization


2. Graph Stucture LearningPermalink

Recent works

  • consider spatial & temporal SEPERATELY


GWN (Graph Wave Net)

  • use adaptive A


STAWnet

  • attention to get self-learned node embedding

    ( to capture spatial embedding )


GWN & STAWnet : use Dilated Causal Convolution


MTGNN

  • learn 2 embedding vectors per node
  • then obtain A


GDN

  • node embedding per node
  • then build kNN graph


AGCRN

  • 2 adaptive modules for enhancing GCN
  • infer dynamic spatial relations


3. MethodologyPermalink

figure2


(1) Graph Structure Learning modulePermalink

a) MGN (Multi-Graph Generation Network)Permalink

  • extract dynamic spatial relationships
  • use difference operation

Diff(X:,1,Xi:,2,Xi,3,,Xi,T)={X:,2X:,1,X:,3Xi,2,,Xi,TXi,T1}{ˆX:,1,ˆXi,2,,ˆX:,T1}.


Considering periodicity of TS, set period P to segment MTS

S=Ttrain /P

  • then, concatenate them!
  • O=[ˆX1,ˆX2ˆXS]RS×N×D×P.


Then, use 2d-conv & FC layer to obtain R graphs

These constitute the graph set A.


b) SSU (Smooth Sparse Unit)Permalink

  • to learn continuous & sparse graphs


2 function : f & φ

  • [smooth function 1] f:RR
    • f(x)={e1x(x>0)0(x0).
  • [smooth function 2] φ:R[0,1]
    • φ(x)=αf(x)αf(x)+f(1x)(αR+).
      • φ(x) 0 for x0
      • φ(x)(0,1) for 0<x<1
      • φ(x)1 for x1.


Output adjacency matrix : A=αf(G)αf(G)+f(1G)

  • GRN×N : output of FC layer in (a)


(2) Temporal Forecasting modulePermalink

a) Graph SelectionPermalink

  • from R graphs, select the best one ( finding optimal graph structure )
  • for each TS Xin RB×Tin×N×D,
    • select the best graph!


Optimal graph : A=argmaxAiAcosXTX,Ai

  • cosX,Y=i,jxijyiji,jx2iji,jy2ij,
  • X=Bi=1Dj=1Xin [i,:,:,j]RTin×N,


figure2

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