The walks are counted on the direct product graph, whose adjacency is
the Kronecker product A1 (x) A2: a walk there is a pair of
walks, one in each graph, of equal length. Convergence needs
lam below 1 / (rho(A1) rho(A2)), a much tighter
constraint than the single-graph case.
Usage
RandW(G1, G2, lam = 0.05)
Arguments
- G1
Square adjacency matrix of the first graph.
- G2
Square adjacency matrix of the second graph.
- lam
Discount factor, positive.
Value
List with estimate, trace, n1, n2.
Details
Formula: k(G1, G2) = sum_ij [(I - lam (A1 (x) A2))^{-1}]_ij.
References
Gaertner, T., Flach, P. & Wrobel, S. (2003). On graph
kernels: hardness results and efficient alternatives. Learning
Theory and Kernel Machines, LNCS 2777, pages 129-143.
doi:10.1007/978-3-540-45167-9_11
.
Examples
RandW(G1 = 5L, G2 = 5L)
#> $estimate
#> [1] -4
#>
#> $trace
#> [1] -4
#>
#> $n1
#> [1] 1
#>
#> $n2
#> [1] 1
#>
#> $method
#> [1] "Direct-product random-walk graph kernel"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
