context("adjacency spectral embedding")
std <- function(x) {
x <- zapsmall(x)
apply(x, 2, function(col) {
if (any(col < 0) && col[which(col != 0)[1]] < 0) { -col } else { col }
})
}
mag_order <- function(x) {
order(abs(x), sign(x), decreasing=TRUE)
}
mag_sort <- function(x) {
x[mag_order(x)]
}
test_that("Undirected, unweighted case works", {
library(igraph)
library(Matrix)
set.seed(42)
g <- random.graph.game(10, 15, type="gnm", directed=FALSE)
no <- 7
A <- g[]
A <- A + 1/2 * as(Matrix(diag(degree(g)), doDiag=FALSE), "generalMatrix")
ss <- eigen(A)
U <- std(ss$vectors)
X <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
au_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=TRUE)
as_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_la$D, equals(ss$values[1:no]))
expect_that(au_la$D, equals(ss$values[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
expect_that(std(au_la$X), equals(X[,1:no]))
au_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=TRUE)
as_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_lm$D, equals(mag_sort(ss$values)[1:no]))
expect_that(au_lm$D, equals(mag_sort(ss$values)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(ss$values)][,1:no])))
expect_that(std(au_lm$X), equals(X[,mag_order(ss$values)][,1:no]))
au_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=TRUE)
as_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_sa$D, equals(ss$values[vcount(g)-1:no+1]))
expect_that(au_sa$D, equals(ss$values[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
expect_that(std(au_sa$X), equals(X[,vcount(g)-1:no+1]))
})
test_that("Undirected, weighted case works", {
library(igraph)
library(Matrix)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=FALSE)
E(g)$weight <- sample(1:5, ecount(g), replace=TRUE)
no <- 3
A <- g[]
A <- A + 1/2 * as(Matrix(diag(degree(g)), doDiag=FALSE), "generalMatrix")
ss <- eigen(A)
U <- std(ss$vectors)
X <- std(ss$vectors %*% sqrt(diag(abs(ss$values))))
au_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=TRUE)
as_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_la$D, equals(ss$values[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
expect_that(au_la$D, equals(ss$values[1:no]))
expect_that(std(au_la$X), equals(X[,1:no]))
au_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=TRUE)
as_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_lm$D, equals(mag_sort(ss$values)[1:no]))
expect_that(au_lm$D, equals(mag_sort(ss$values)[1:no]))
expect_that(std(as_lm$X), equals(std(U[,mag_order(ss$values)][,1:no])))
expect_that(std(au_lm$X), equals(X[,mag_order(ss$values)][,1:no]))
au_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=TRUE)
as_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=FALSE)
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
expect_that(std(au_sa$X), equals(X[,vcount(g)-1:no+1]))
})
test_that("Directed, unweighted case works", {
library(igraph)
library(Matrix)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=TRUE)
no <- 3
A <- g[]
A <- A + 1/2 * as(Matrix(diag(degree(g)), doDiag=FALSE), "generalMatrix")
ss <- svd(A)
U <- std(ss$u)
V <- std(ss$v)
X <- std(ss$u %*% sqrt(diag(ss$d)))
Y <- std(ss$v %*% sqrt(diag(ss$d)))
au_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=TRUE)
as_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_la$D, equals(ss$d[1:no]))
expect_that(au_la$D, equals(ss$d[1:no]))
expect_that(std(as_la$X), equals(std(U[,1:no])))
expect_that(std(as_la$Y), equals(std(V[,1:no])))
expect_that(std(au_la$X), equals(X[,1:no]))
expect_that(std(au_la$Y), equals(Y[,1:no]))
au_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=TRUE)
as_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_lm$D, equals(ss$d[1:no]))
expect_that(au_lm$D, equals(ss$d[1:no]))
expect_that(std(as_lm$X), equals(std(U[,1:no])))
expect_that(std(as_lm$Y), equals(std(V[,1:no])))
expect_that(std(au_lm$X), equals(X[,1:no]))
expect_that(std(au_lm$Y), equals(Y[,1:no]))
au_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=TRUE)
as_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=FALSE)
expect_that(as_sa$D, equals(ss$d[vcount(g)-1:no+1]))
expect_that(au_sa$D, equals(ss$d[vcount(g)-1:no+1]))
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
expect_that(std(as_sa$Y), equals(std(V[,vcount(g)-1:no+1])))
expect_that(std(au_sa$X), equals(X[,vcount(g)-1:no+1]))
expect_that(std(au_sa$Y), equals(Y[,vcount(g)-1:no+1]))
})
test_that("Directed, weighted case works", {
library(igraph)
library(Matrix)
set.seed(42)
g <- random.graph.game(10, 20, type="gnm", directed=TRUE)
E(g)$weight <- sample(1:5, ecount(g), replace=TRUE)
no <- 3
A <- g[]
A <- A + 1/2 * as(Matrix(diag(degree(g)), doDiag=FALSE), "generalMatrix")
ss <- svd(A)
U <- std(ss$u)
V <- std(ss$v)
X <- std(ss$u %*% sqrt(diag(ss$d)))
Y <- std(ss$v %*% sqrt(diag(ss$d)))
au_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=TRUE)
as_la <- embed_adjacency_matrix(g, no=no, which="la",
cvec=degree(g)/2, scaled=FALSE)
expect_that(std(as_la$X), equals(std(U[,1:no])))
expect_that(std(as_la$Y), equals(std(V[,1:no])))
expect_that(std(au_la$X), equals(X[,1:no]))
expect_that(std(au_la$Y), equals(Y[,1:no]))
au_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=TRUE)
as_lm <- embed_adjacency_matrix(g, no=no, which="lm",
cvec=degree(g)/2, scaled=FALSE)
expect_that(std(as_lm$X), equals(std(U[,1:no])))
expect_that(std(as_lm$Y), equals(std(V[,1:no])))
expect_that(std(au_lm$X), equals(X[,1:no]))
expect_that(std(au_lm$Y), equals(Y[,1:no]))
au_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=TRUE)
as_sa <- embed_adjacency_matrix(g, no=no, which="sa",
cvec=degree(g)/2, scaled=FALSE)
expect_that(std(as_sa$X), equals(std(U[,vcount(g)-1:no+1])))
expect_that(std(as_sa$Y), equals(std(V[,vcount(g)-1:no+1])))
expect_that(std(au_sa$X), equals(X[,vcount(g)-1:no+1]))
expect_that(std(au_sa$Y), equals(Y[,vcount(g)-1:no+1]))
})
test_that("Issue #50 is resolved", {
library(igraph)
set.seed(12345)
g <- erdos.renyi.game(15, .4)
w <- -log(runif(ecount(g)))
X1 <- embed_adjacency_matrix(g, 2, weights= w)
E(g)$weight <- w
X2 <- embed_adjacency_matrix(g, 2)
expect_that(X1$D, equals(X2$D))
})
test_that("Issue #51 is resolved", {
library(igraph)
set.seed(12345)
pref.matrix <- diag(0.2, 2) + 0.2
block.sizes <- c(800, 800)
n <- sum(block.sizes)
g <- sbm.game(n, pref.matrix, block.sizes, directed=TRUE)
for (i in 1:25) {
ase <- embed_adjacency_matrix(g, 2)
expect_that(mean(ase$X %*% t(ase$Y)), equals(0.299981018354173))
}
})
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