Personalised propagation of neural predictions

Ahat = Dtilde^{-1/2}(A + I)Dtilde^{-1/2}; Z = alpha (I - (1-alpha) Ahat)^{-1} H (PPNP), or K steps of Z <- (1-alpha) Ahat Z + alpha H from Z = H (APPNP), with a row-wise softmax on the last step.

Usage

Appnp(A, H, alpha = 0.1, K = 10, exact = FALSE, softmax = TRUE)

Arguments

A

Adjacency matrix without self-loops; symmetrised internally.

H

Per-node predictions, one row per node.

alpha

Teleport probability in (0, 1].

K

Power-iteration steps.

exact

Use the closed-form PPNP inverse.

softmax

Apply the row-wise softmax.

Value

List with Z, alpha, K, exact, n, c.

References

Klicpera, Bojchevski and Guennemann (2019), ICLR; arXiv:1810.05997, Sect. 3. Read from the ar5iv rendering.

Examples

set.seed(1)
A <- matrix(c(0, 1, 0, 1, 0, 1, 0, 1, 0), 3, 3, byrow = TRUE)
H <- matrix(rnorm(6), 3, 2)
Appnp(A, H)
#> $Z
#>           [,1]      [,2]
#> [1,] 0.2832692 0.7167308
#> [2,] 0.3133624 0.6866376
#> [3,] 0.3713353 0.6286647
#> 
#> $alpha
#> [1] 0.1
#> 
#> $K
#> [1] 10
#> 
#> $exact
#> [1] FALSE
#> 
#> $n
#> [1] 3
#> 
#> $c
#> [1] 2
#> 
#> $method
#> [1] "APPNP personalised-PageRank propagation (Klicpera et al. 2019)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"