Graph convolution with the renormalisation trick

Adding the self-loop before normalising keeps the eigenvalues of the propagation operator inside [-1, 1], which is what stops repeated application from exploding.

Usage

GcnL(A, X, W)

Arguments

A

Square adjacency matrix.

X

Node feature matrix, one row per node.

W

Weight matrix, one row per input feature.

Value

List with estimate, H, preactivation, n, method.

Details

Formula: H' = relu(Dt^{-1/2} (A + I) Dt^{-1/2} X W), Dt = diag(rowSums(A + I)).

References

Kipf and Welling (2017), ICLR 2017, eqs. (2) and (8). arXiv:1609.02907

Examples

set.seed(1)
A <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3, byrow = TRUE)
X <- matrix(rnorm(6), 3, 2)
W <- matrix(rnorm(4), 2, 2)
GcnL(A, X, W)
#> $estimate
#> [1] 0.1042731
#> 
#> $H
#>            [,1] [,2]
#> [1,] 0.57210545    0
#> [2,] 0.05353326    0
#> [3,] 0.00000000    0
#> 
#> $preactivation
#>             [,1]       [,2]
#> [1,]  0.57210545 -0.4218540
#> [2,]  0.05353326 -0.4385753
#> [3,] -0.37067714 -0.1132026
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "H' = relu(Dt^{-1/2}(A+I)Dt^{-1/2} X W), Kipf & Welling (2017) eq. (8)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"