ChebNet spectral filter — Gcnchb • rmorie

The Chebyshev recurrence is what makes the filter K-localised and costs only K sparse products. lambda_max comes from the Jacobi eigenvalues of the supplied symmetric Laplacian; with no coefficients passed the deterministic choice theta_k = 1/(k+1) is used.

Usage

Gcnchb(L, X, K = 3, theta = NULL)

Arguments

L: Symmetric graph Laplacian.
X: Node feature matrix, one row per node.
K: Filter order (number of Chebyshev terms).
theta: Optional length-K coefficient vector.

Value

List with estimate, H, lambda_max, K, n, method.

Details

Formula: sum_{k=0}^{K-1} theta_k T_k(Lt) X, Lt = 2 L / lambda_max - I, T_k = 2 Lt T_{k-1} - T_{k-2}, T_0 = I, T_1 = Lt.

References

Defferrard, Bresson and Vandergheynst (2016), Convolutional neural networks on graphs with fast localized spectral filtering, NIPS 29, eqs. (4)-(5). arXiv:1606.09375

Examples

Gcnchb(L = 5L, X = 5L)
#> $estimate
#> [1] 9.166667
#> 
#> $H
#>          [,1]
#> [1,] 9.166667
#> 
#> $lambda_max
#> [1] 5
#> 
#> $K
#> [1] 3
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "sum_k theta_k T_k(2L/lmax - I) X, Defferrard et al. (2016) eqs. (4)-(5)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"